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It is well known that the full compressible Navier-Stokes equations can be deduced via the Chapman-Enskog expansion from the Boltzmann equation as the first-order correction to the Euler equations with viscosity and heat-conductivity coefficients of order of the Knudsen number ε >0. In the paper, we carry out the rigorous mathematical analysis of the compressible Navier-Stokes approximation for the Boltzmann equation regarding the initial-boundary value problems in general bounded domains. The main goal is to measure the uniform-in-time deviation of the Boltzmann solution with diffusive reflection boundary condition from a local Maxwellian with its fluid quantities given by the solutions to the corresponding compressible Navier-Stokes equations with consistent non-slip boundary conditions whenever ε > 0 is small enough. Specifically, it is shown that for well chosen initial data around constant equilibrium states, the deviation weighted by a velocity function is O(ε1/2) in L∞x,v and O(ε3/2) in L2x,v globally in time. The proof is based on the uniform estimates for the remainder in different functional spaces without any spatial regularity. One key step is to obtain the global-in-time existence as well as uniform-in-ε estimates for regular solutions to the full compressible Navier-Stokes equations in bounded domains when the parameter ε > 0 is involved in the analysis. [ABSTRACT FROM AUTHOR]

In the first author's Math. Res. Lett. paper (2014), the quasi-Frobenius-Lusztig kernel associated with 5/2 was constructed. In this paper we construct the quasi-Frobenius-Lusztig kernels associated with any simple Lie algebra g. [ABSTRACT FROM AUTHOR]

This paper serves as a source of examples of Rokhlin actions or locally representable actions of finite groups on C*-algebras satisfying a certain UHF-absorption condition. We show that given any finite group G and a separable, unital C*-algebra A that absorbs M|G|∞ tensorially, one can lift any group homomorphism G → Aut(A)/≈u to an honest Rokhlin action γ of G on A. Unitality may be dropped in favour of stable rank one or being stable. If A belongs to a certain class of C*-algebras that is classifiable by a suitable invariant (e.g. K-theory), then in fact every G-action on the invariant lifts to a Rokhlin action of G on A. For the crossed product C*-algebra A ⋊γ G of a Rokhlin action on a UHF-absorbing C*-algebra, an inductive limit decomposition is obtained in terms of A and γ. If G is assumed to be abelian, then the dual action ˆγ is locally representable in a very strong sense. We then show how some well-known constructions of finite group actions with certain predescribed properties can be recovered and extended by the main results of this paper when paired with known classification theorems. Among these is Blackadar's famous construction of symmetries on the CAR algebra whose fixed point algebras have non-trivial K1-groups. Lastly, we use the results of this paper to reduce the UCT problem for separable, nuclear C*-algebras to a question about certain finite group actions on O2. [ABSTRACT FROM AUTHOR]

We show that general triple planes with genus and irregularity zero belong to at most 12 families, that we call surfaces of type I to XII, and we prove that the corresponding Tschirnhausen bundle is a direct sum of two line bundles in cases I, II, III, whereas it is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit descriptions for surfaces of type I to VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski. Finally, in the last part of the paper we discuss some moduli problems related to our constructions. [ABSTRACT FROM AUTHOR]

In this paper we introduce new densities on the set of primes of a number field. If K/K0 is a Galois extension of number fields, we associate to any element x ∈ ... a density δK/K0,x on the primes of K. In particular, the density associated to x = 1 is the usual Dirichlet density on K. We also give two applications of these densities (for x ≠ 1): the first is a realization result à la the Grunwald-Wang theorem such that essentially, ramification is only allowed in a set of arbitrarily small (positive) Dirichlet density. The second concerns the so-called saturated sets of primes, introduced by Wingberg. [ABSTRACT FROM AUTHOR]

In this paper we study various "abscissae" which one can associate to a given function f, or rather to the power moments of f. These are motivated by long-standing open problems in analytic number theory. We show how these abscissae connect to the distribution of values of f in a very elegant way using convex conjugates. This connection allows us to show which abscissae are realizable for both general and more specific arithmetical functions. Further it may give a new approach to, for example, Dirichlet's divisor problem. [ABSTRACT FROM AUTHOR]

For a finite group G and an arbitrary commutative ring R, Broué has placed a Frobenius exact structure on the category of finitely generated RG-modules by taking the exact sequences to be those that split upon restriction to the trivial subgroup. The corresponding stable category is then tensor triangulated. In this paper we examine the case R = S/tn, where S is a discrete valuation ring having uniformising parameter t. We prove that the prime ideal spectrum (in the sense of Balmer) of this 'relative' version of the stable module category of RG is a disjoint union of n copies of that for kG, where k is the residue field of S. [ABSTRACT FROM AUTHOR]

At the 1987 Ramanujan Centenary meeting Dyson asked for a coherent group-theoretical structure for Ramanujan's mock theta functions analogous to Hecke's theory of modular forms. Many of Ramanujan's mock theta functions can be written in terms of R(ζ, q), where R(z, q) is the two-variable generating function of Dyson's rank function and ζ is a root of unity. Building on earlier work of Watson, Zwegers, Gordon, and McIntosh, and motivated by Dyson's question, Bringmann, Ono, and Rhoades studied transformation properties of R(ζ, q). In this paper we strengthen and extend the results of Bringmann, Rhoades, and Ono, and the later work of Ahlgren and Treneer. As an application we give a new proof of Dyson's rank conjecture and show that Ramanujan's Dyson rank identity modulo 5 from the Lost Notebook has an analogue for all primes greater than 3. The proof of this analogue was inspired by recent work of Jennings-Shaffer on overpartition rank differences mod 7. [ABSTRACT FROM AUTHOR]

In this paper, we derive a function field version of theWaldspurger formula for the central critical values of the Rankin-Selberg L-functions. This formula states that the central critical L-values in question can be expressed as the "ratio" of the global toric period integral to the product of the local toric period integrals. Consequently, this result provides a necessary and sufficient criterion for the non-vanishing of these central critical L-values, and supports the Gross-Prasad conjecture for SO(3) over function fields. [ABSTRACT FROM AUTHOR]

Let μ be a Borel measure on a compactum X. The main objects in this paper are s-ideals Ipdimq, J0pμq, Jf pμq of Borel sets in X that can be covered by countably many compacta which are finite-dimensional, or of μ-measure null, or of finite μ-measure, respectively. Answering a question of J. Zapletal, we shall show that for the Hilbert cube, the s-ideal Ipdimq is not homogeneous in a strong way. We shall also show that in some natural instances of measures μ with nonhomogeneous s-ideals J0pμq or Jf pμq, the completions of the quotient Boolean algebras BorelpXq{J0pμq or BorelpXq{Jf pμq may be homogeneous. We discuss the topic in a more general setting, involving calibrated s-ideals. [ABSTRACT FROM AUTHOR]

In the 1960s Maurice Auslander proved the following important result. Let R be the commutative polynomial ring C[x1, . . ., xn], and let G be a finite small subgroup of GLn(C) acting on R naturally. Let A be the fixed subring RG:= {a ∈ R|g(a) = a for all g ∈ G}. Then the endomorphism ring of the right A-module RA is naturally isomorphic to the skew group algebra R* G. In this paper, a version of the Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite-dimensional Lie algebras, and (c) noetherian graded down-up algebras. [ABSTRACT FROM AUTHOR]

A quasi-infinitely divisible distribution on R is a probability distribution whose characteristic function allows a L'evy-Khintchine type representation with a "signed L'evy measure", rather than a L'evy measure. Quasiinfinitely divisible distributions appear naturally in the factorization of infinitely divisible distributions. Namely, a distribution μ is quasi-infinitely divisible if and only if there are two infinitely divisible distributions μ1 and μ2 such that μ1 * μ = μ2. The present paper studies certain properties of quasiinfinitely divisible distributions in terms of their characteristic triplet, such as properties of supports, finiteness of moments, continuity properties, and weak convergence, with various examples constructed. In particular, it is shown that the set of quasi-infinitely divisible distributions is dense in the set of all probability distributions with respect to weak convergence. Further, it is proved that a distribution concentrated on the integers is quasi-infinitely divisible if and only if its characteristic function does not have zeroes, with the use of the Wiener-L'evy theorem on absolutely convergent Fourier series. A number of fine properties of such distributions are proved based on this fact. A similar characterization is not true for nonlattice probability distributions on the line. [ABSTRACT FROM AUTHOR]

In this paper, we establish the following reverse Stein-Weiss inequality, namely the reversed weighted Hardy-Littlewood-Sobolev inequality, in Rn: ... for any nonnegative functions ... and ... such that .... We derive the existence of extremal functions for the above inequality. Moreover, some asymptotic behaviors are obtained for the corresponding Euler-Lagrange system. For an analogous weighted system, we prove necessary conditions of existence for any positive solutions by using the Pohozaev identity. Finally, we also obtain the corresponding Stein-Weiss and reverse Stein-Weiss inequalities on the ndimensional sphere Sn by using the stereographic projections. Our proof of the reverse Stein-Weiss inequalities relies on techniques in harmonic analysis and differs from those used in the proof of the reverse (non-weighted) Hardy-Littlewood-Sobolev inequalities. [ABSTRACT FROM AUTHOR]

In Theorem 3.1 of The rigidity theorems of self-shrinkers (2014), the author and Y. L. Xin proved a rigidity result for self-shrinkers under the integral condition on the norm of the second fundamental form. In this paper, we relax such a bound to any finite constant (see Theorem 4.4 for details). [ABSTRACT FROM AUTHOR]

In this paper, we show that the chordal Loewner differential equation with C° driving function generates a C°1/2 slit for 1/2 < ° ≼ 2, except when ° = 3/2 the slit is only proved to be weakly C1,1. [ABSTRACT FROM AUTHOR]

In this paper we first construct a two-variable p-adic L-function for the standard representation associated with a Hida family of parallel weight genus g Siegel forms, using a method developed by Böcherer-Schmidt in one variable. When a form f has weight g + 1 a non-crystalline trivial zero could appear. In this case, using the two-variable p-adic L-function we have constructed, we can apply the method of Greenberg-Stevens to calculate the first derivative of the p-adic L-function for f and show that it has the form predicted by a conjecture of Greenberg on trivial zeros. [ABSTRACT FROM AUTHOR]

In [J. Inst. Math. Jussieu 14 (2015), 149-184] and [Int. Math. Res. Not. IMRN 7 (2017), 2014-2099] a family of Rankin-Selberg integrals was shown to represent the twisted standard L-function L(s, π, χ, st) of a cuspidal representation π of the exceptional group of type G2. These integral representations bind the analytic behavior of this L-function with that of a family of degenerate Eisenstein series for quasi-split forms of Spin8 associated to an induction from a character on the Heisenberg parabolic subgroup. This paper is divided into two parts. In Part 1 we study the poles of these degenerate Eisenstein series in the right half-plane Re(s) > 0. In Part 2 we use the results of Part 1 to prove the conjecture, made by J. Hundley and D. Ginzburg in [Israel J. Math. 207 (2015), 835-879], for stable poles and also to give a criterion for π to be a CAP representation with respect to the Borel subgroup of G2 in terms of the analytic behavior of L(s, π, χ, st) at s = 3/2. [ABSTRACT FROM AUTHOR]

Let G be a simple algebraic group of exceptional type, over an algebraically closed field of characteristic p = 0. A closed subgroup H of G is called G-completely reducible (G-cr) if whenever H is contained in a parabolic subgroup P of G, it is contained in a Levi subgroup of P. In this paper we determine the G-conjugacy classes of non-G-cr simple connected subgroups of G when p is good for G. For each such subgroup X, we determine the action of X on the adjoint module L(G) and the connected centraliser of X in G. As a consequence we classify all non-G-cr connected reductive subgroups of G, and determine their connected centralisers. We also classify the subgroups of G which are maximal among connected reductive subgroups, but not maximal among all connected subgroups. [ABSTRACT FROM AUTHOR]

In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath in a more general setting and also relate to recent work of Gressman. In particular, we establish optimisers for these determinant inequalities. We then use these inequalities to establish our Main Theorem, which gives a geometric inequality of matrix type which improves and extends some inequalities of Christ. [ABSTRACT FROM AUTHOR]

This is the fourth paper in a series. We prove a conjecture made independently by Boston et al. and Shalev. The conjecture asserts that there is an absolute positive constant δ such that if G is a finite simple group acting transitively on a set of size n > 1, then the proportion of derangements in G is greater than δ. We show that with possibly finitely many exceptions, one can take δ = .016. Indeed, we prove much stronger results showing that for many actions, the proportion of derangements tends to 1 as n increases and we prove similar results for families of permutation representations. [ABSTRACT FROM AUTHOR]

This paper investigates lower bounds on the number of zeros and poles of a general Dirichlet series in a disk of radius r and gives, as a consequence, an affirmative answer to an open problem of Bombieri and Perelli on the bound. Applications will also be given to Picard type theorems, global estimates on the symmetric difference of zeros, and uniqueness problems for Dirichlet series. [ABSTRACT FROM AUTHOR]

We construct an example of a unit-regular ring which is not strongly clean, answering an open question of Nicholson. We also characterize clean matrices with a zero column, and this allows us to describe an interesting connection between unit-regular elements and clean elements. Next we study in arbitrary rings those elements whose powers are regular, and provide a method for constructing inner inverses which satisfy many additional strong relations. As a corollary we show that if each of the powers a, a², ..., an is a regular element in some ring R (for some n ≥ 1), then there exists w ∈ R such that akwkak = ak and wkakwk = wk for 1 ≤ k ≤ n. Similar statements are also obtained for unit-regular elements. The paper ends with a large number of examples elucidating further connections (and disconnections) between cleanness, regularity, and unit-regularity. [ABSTRACT FROM AUTHOR]

Let G be a connected reductive algebraic group over an algebraically closed field k. In a recent paper, Bate, Martin, Röhrle and Tange show that every (smooth) subgroup of G is separable provided that the characteristic of k is very good for G. Here separability of a subgroup means that its scheme-theoretic centralizer in G is smooth. Serre suggested extending this result to arbitrary, possibly non-smooth, subgroup schemes of G. The aim of this paper is to prove this more general result. Moreover, we provide a condition on the characteristic of k that is necessary and sufficient for the smoothness of all centralizers in G. We finally relate this condition to other standard hypotheses on connected reductive groups. [ABSTRACT FROM AUTHOR]

Extending the methods developed in the author's recent paper and using some techniques from a paper by Sogge and Stein in conjunction with various facts about adapted coordinate systems in two variables, an Lp boundedness theorem is proven for maximal operators over hypersurfaces in R³ when p > 2. When the best possible p is greater than 2, the theorem typically provides sharp estimates. This gives another approach to the subject of recent work of Ikromov, Kempe, and Müller (2010). [ABSTRACT FROM AUTHOR]

Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space. This paper investigates iterated function systems consisting of Möbius transformations on the extended complex plane or, equivalently, on the Riemann sphere. The main result is a characterization, in terms of topological, geometric, and dynamical properties, of Möbius iterated function systems that possess an attractor. The paper also includes results on the duality between the attractor and repeller of a Möbius iterated function system. [ABSTRACT FROM AUTHOR]

Abstract notions of "smallness" are among the most important tools that model theory offers for the analysis of arbitrary structures. The two most useful notions of this kind are forking (which is closely related to certain measure zero ideals) and thorn-forking (which generalizes the usual topological dimension). Under certain mild assumptions, forking is the finest notion of smallness, whereas thorn-forking is the coarsest. In this paper we study forking and thorn-forking, restricting ourselves to the class of generically stable types. Our main conclusion is that in this context these two notions coincide. We explore some applications of this equivalence. [ABSTRACT FROM AUTHOR]

This paper contains the construction, examples and properties of a trace and a trace pairing for certain morphisms in a monoidal category with switching isomorphisms. Our construction of the categorical trace is a common generalization of the trace for endomorphisms of dualizable objects in a balanced monoidal category and the trace of nuclear operators on a topological vector space with the approximation property. In a forthcoming paper, applications to the partition function of super-symmetric field theories will be given. [ABSTRACT FROM AUTHOR]

In this paper we study the derivative at the center of symmetry of an incoherent Eisenstein series which is associated to an imaginary quadratic field. We show that each nonconstant Fourier coefficient of the derivative can be expressed as the degree of certain zero cycles on a moduli scheme. This result is a generalization of the work by Kudla-Rapoport-Yang. [ABSTRACT FROM AUTHOR]

In this paper, following J. Franks' work on Lyapunov graphs of nonsingular Smale flows on S³, we study Lyapunov graphs of nonsingular Smale flows on S¹ ×S². More precisely, we determine necessary and sufficient conditions on an abstract Lyapunov graph to be associated with a nonsingular Smale flow on S¹ ×S². We also study the singular type vertices in Lyapunov graphs of nonsingular Smale flows on 3-manifolds. [ABSTRACT FROM AUTHOR]

In this paper we study entire solutions of the Allen-Cahn equation Δu - F'(u) = 0, where F is an even, bistable function. We are particularly interested in the description of the moduli space of solutions which have some special structure at infinity. The solutions we are interested in have their zero set asymptotic to 2k, k&#8805 2 oriented affine half-lines at infinity and, along each of these affine half-lines, the solutions are asymptotic to the one-dimensional heteroclinic solution: such solutions are called multiple-end solutions, and their set is denoted by MM2k. The main result of our paper states that if u ∈ M2k is nondegenerate, then locally near u the set of solutions is a smooth manifold of dimension 2k. This paper is part of a program whose aim is to classify all 2k-ended solutions of the Allen-Cahn equation in dimension 2, for k ≥ 2. [ABSTRACT FROM AUTHOR]

This paper gives two results on the simple modules for the Brauer algebra Bn(d) over the complex field. First we describe the module structure of the restriction of all simple Bn(d)-modules to Bn-1(d). Second we give a new geometrical interpretation of Ram and Wenzl's construction of bases for "d-permissible" simple modules. [ABSTRACT FROM AUTHOR]

This paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded if and only if the almost fiber part is aspiral, and in this case, the subsurface is virtually a leaf of a taut foliation. Besides other consequences, examples are exhibited that nongeometric 3-manifolds with no Seifert fibered pieces may contain essentially immersed but not virtually embedded closed subsurfaces. [ABSTRACT FROM AUTHOR]

Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness at finite and infinite minimal Martin boundary points for a large class of purely discontinuous symmetric Lévy processes. [ABSTRACT FROM AUTHOR]

This paper begins the study of relations between Riemannian geometry and contact topology on (2n + 1)-manifolds and continues this study on 3-manifolds. Specifically we provide a lower bound for the radius of a geodesic ball in a contact (2n+ 1)-manifold (M, ξ) that can be embedded in the standard contact structure on R2n+1, that is, on the size of a Darboux ball. The bound is established with respect to a Riemannian metric compatible with an associated contact form a for ξ. In dimension 3, this further leads us to an estimate of the size for a standard neighborhood of a closed Reeb orbit. The main tools are classical comparison theorems in Riemannian geometry. In the same context, we also use holomorphic curve techniques to provide a lower bound for the radius of a PS-tight ball. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonlinear Schrödinger equation iut + Δu = λ|u| 4/N-4u in RN, N = 5, with λ ∈ C. We prove local well-posedness (local existence, unconditional uniqueness, continuous dependence) in the critical space H²(RN). [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three- dimensional generic shrinking Ricci soliton is given by quotients of either S³, RS² or R³ under some very weak conditions on the vector field X generating the soliton structure. In doing so we introduce analytical tools that could be useful in other settings; for instance we prove that the Omori-Yau maximum principle holds for the X-Laplacian on every generic Ricci soliton without any assumption on X. [ABSTRACT FROM AUTHOR]

In this paper, as a main result, we derive a Chung-Fuchs type condition for the recurrence of Feller processes associated with pseudo-differential operators. In the Lévy process case, this condition reduces to the classical and well-known Chung-Fuchs condition. Further, we also discuss the recurrence and transience of Feller processes with respect to the dimension of the state space and Pruitt indices and the recurrence and transience of Feller-Dynkin diffusions and stable-like processes. Finally, in the one-dimensional symmetric case, we study perturbations of Feller processes which do not affect their recurrence and transience properties, and we derive sufficient conditions for their recurrence and transience in terms of the corresponding Lévy measure. In addition, some comparison conditions for recurrence and transience also in terms of the Lévy measures are obtained. [ABSTRACT FROM AUTHOR]

A geometric categorification is given for arbitrary-large-finitedimensional quotients of quantum osp(1/2) and tensor products of its simple modules. The modified quantum osp(1/2) of Clark-Wang, a new version in this paper and the modified quantum sl(2) are shown to be isomorphic to each other over a field containing Q(v) and √-1. [ABSTRACT FROM AUTHOR]

In this paper, by combining modularity of the Witten genus and the modular forms constructed by Liu and Wang, we establish mod 3 congruence properties of certain twisted signatures of 24 dimensional string manifolds. [ABSTRACT FROM AUTHOR]

This paper concerns the first passage times to a point a > 0, denoted by σa, of Bessel processes. We are interested in the case when the process starts at x > a and we compute the densities of the distributions of aa to obtain the exact asymptotic forms of them as t → < ∞ that are valid uniformly in x > a for every order of the Bessel process. [ABSTRACT FROM AUTHOR]

Let F be a quadratic form in N ≥ 2 variables defined on a vector space V ⊆ KN over a global field K, and Ƶ ⊆ KN be a finite union of varieties defined by families of homogeneous polynomials over K. We show that if V \ Ƶ contains a nontrivial zero of F, then there exists a linearly independent collection of small-height zeros of F in V \ Ƶ, where the height bound does not depend on the height of Ƶ, only on the degrees of its defining polynomials. As a corollary of this result, we show that there exists a small-height maximal totally isotropic subspace W of the quadratic space (V, F) such that W is not contained in Ƶ. Our investigation extends previous results on small zeros of quadratic forms, including Cassels' theorem and its various generalizations. The paper also contains an appendix with two variations of Siegel's lemma. All bounds on height are explicit. [ABSTRACT FROM AUTHOR]

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the compact operators.) In this paper we establish that the analogous conclusion holds for a broad family of quotient algebras. Specifically, we will show that assuming the Continuum Hypothesis, if A is a separable algebra which is either simple or stable, then the corona of A has nontrivial automorphisms. We also discuss a connection with cohomology theory, namely, that our proof can be viewed as a computation of the cardinality of a particular derived inverse limit. [ABSTRACT FROM AUTHOR]

The object of study in this paper is the on-shell scattering matrix S(E) of the Schrödinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of S(E) in the semiclassical limit when the energy parameter E varies from Eres - e to Eres + e, where Eres is a real part of a resonance and e is sufficiently small. The main result of our work describes the spectral flow of the scattering matrix through a given point on the unit circle. This result is closely related to the Breit-Wigner effect. [ABSTRACT FROM AUTHOR]

Let A be a graded algebra. In this paper we develop a generalized Koszul theory by assuming that A0 is self-injective instead of semisimple and generalize many classical results. The application of this generalized theory to directed categories and finite EI categories is described. [ABSTRACT FROM AUTHOR]

In this paper we study exceptional Dehn fillings on hyperbolic knot manifolds which contain an essential once-punctured torus. Let M be such a knot manifold and let β be the boundary slope of such an essential once-punctured torus. We prove that if Dehn filling M with slope α produces a Seifert fibred manifold, then Δ(α, β) ≤ 5. Furthermore we classify the triples (M; α, β) when Δ(α, β) ≥ 4. More precisely, when Δ(α, β) = 5, then M is the (unique) manifold W h(-3/2) obtained by Dehn filling one boundary component of the Whitehead link exterior with slope -3/2, and (α, β) is the pair of slopes (-5, 0). Further, Δ(α, β) = 4 if and only if (M; α, β) is the triple (Wh(-2n ± 1/n);-4, 0) for some integer n with |n| > 1. Combining this with known results, we classify all hyperbolic knot manifolds M and pairs of slopes (β, γ) on ∂M where β is the boundary slope of an essential once-punctured torus in M and γ is an exceptional filling slope of distance 4 or more from β. Refined results in the special case of hyperbolic genus one knot exteriors in S³ are also given. [ABSTRACT FROM AUTHOR]

Among all classes of pseudo-differential operators only the Weyl operators enjoy the property of symplectic covariance with respect to conjugation by elements of the metaplectic group. In this paper we show that there is, however, a weaker form of symplectic covariance for Shubin's t-dependent operators, in which the intertwiners are no longer metaplectic, but are still invertible non-unitary operators. We also study the case of Born-Jordan operators, which are obtained by averaging the t-operators over the interval [0, 1] (such operators have recently been studied by Boggiatto and his collaborators, and by Toft). We show that covariance still holds for these operators with respect to a subgroup of the metaplectic group. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for L-functions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Roton. As a concrete application, we get, for example, a Beurling-Nyman type criterion for the Siegel zero problem. [ABSTRACT FROM AUTHOR]

In an earlier paper, we introduced the notion of full quivers of representations of algebras, which are more explicit than quivers of algebras. Here, we consider full quivers (as well as pseudo-quivers) as a combinatoric tool in order to describe PI-varieties of algebras. Each full quiver is naturally associated to a polynomial that encapsulates trace-like properties of the underlying algebra. [ABSTRACT FROM AUTHOR]

A key tool in the study of algebraic surfaces and their moduli is Brieskorn's simultaneous resolution for families of algebraic surfaces with simple (du Val or ADE) singularities. In this paper we show that a similar statement holds for families of curves with at worst simple (ADE) singularities. For a family X → B of ADE curves, we give an explicit and natural resolution of the rational map B ⤏ M̅g. Moreover, we discuss a lifting of this map to the moduli stack M̅g, i.e. a simultaneous semi-stable reduction for the family X/B. In particular, we note that in contrast to what might be expected from the case of surfaces, the natural Weyl cover of B is not a sufficient base change for a lifting of the map B ⤏ M̅g to M̅g. [ABSTRACT FROM AUTHOR]

Let l ≥ 5 be prime, let m ≥ 1 be an integer, and let p(n) denote the partition function. Folsom, Kent, and Ono recently proved that there exists a positive integer be(m) of size roughly m² such that the module formed from the Z/lmZ-span of generating functions for p ... with odd b ≥ be(m) has finite rank. The same result holds with "odd" b replaced by "even" b. Furthermore, they proved an upper bound on the ranks of these modules. This upper bound is independent of m; it is .... In this paper, we prove, with a mild condition on l, that be(m) ≤ 2m - 1. Our bound is sharp in all computed cases with l ≥ 29. To deduce it, we prove structure theorems for the relevant Z/lmZ-modules of modular forms. This work sheds further light on a question of Mazur posed to Folsom, Kent, and Ono. [ABSTRACT FROM AUTHOR]