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255 results on '"Benoist, Yves"'

1. Fourier transform in cyclic groups

Author

Benoist, Yves

Subjects
Mathematics - Number Theory
Abstract

On a cyclic group of prime order, the non-trivial Dirichlet characters together with their Fourier transforms have constant modulus outside 0 and vanish at 0. Answering a question of H. Cohn, we construct new functions with these properties. The proof relies on Floer homology. We also apply this method to the biunimodular functions problem., Comment: This version 2 contains a new chapter "Unimodular C-functions for safe prime" that deal with H. Cohn's question for safe primes

Published
2024

2. Convolution and square in abelian groups III

Author

Benoist, Yves

Subjects
Mathematics - Number Theory
Abstract

In the first paper we proved that on the cyclic groups of odd order d, there exist non zero functions whose convolution square f*f(2t) is proportional to their square f(t)^2 when the proportionality constant is an odd algebraic integer of norm d whose both real and imaginary part are square roots of integers. We show here that the function f can be chosen to be equal to the conjugate of its Fourier transform.

Published
2024

3. Bounded harmonic maps

Author

Benoist, Yves and Hulin, Dominique

Subjects
Mathematics - Differential Geometry
Abstract

The classical Fatou theorem identifies bounded harmonic functions on the unit disk with bounded measurable functions on the boundary circle. We extend this theorem to bounded harmonic maps.

Published
2023

4. On the rational symplectic group

Author

Benoist, Yves

Subjects
Mathematics - Group Theory
Abstract

This note contains a short proof of a classical result: any rational symplectic matrix can be put in diagonal form after right and left multiplication by integral symplectic matrices.

Published
2022

5. Convolution and square in abelian groups II

Author

Benoist, Yves

Subjects
Mathematics - Algebraic Geometry
Abstract

A critical value on an abelian group G of odd order d is a value $\lambda$ such that the functional equation f$\star$f (2 t) = $\lambda$f (t)^2 on G has a nonzero solution f. We construct many critical values by using abelian varieties with complex multiplication.

Published
2022

6. Temperedness criterion of the tensor product of parabolic induction for $GL_n$

Author

Benoist, Yves, Inoue, Yui, and Kobayashi, Toshiyuki

Subjects
Mathematics - Representation Theory, 22E46
Abstract

We give a necessary and sufficient condition for a pair of parabolic subgroups $P$ and $Q$ of $G=GL_n(\mathbb{R})$ such that the tensor product of any two unitarily induced representations from $P$ and $Q$ are tempered. We also give an $L^p$-estimate of matrix coefficients of the regular representations on $L^2(G/L)$ when $L$ is a Levi subgroup of $G$., Comment: Final version, to appear in Journal of Algebra

Published
2021
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7. How far are p-adic Lie groups from algebraic groups?

Author

Benoist, Yves and Quint, Jean-François

Subjects
Mathematics - Group Theory
Abstract

We show that, in a weakly regular $p$-adic Lie group $G$, the subgroup $G_u$ spanned by the one-parameter subgroups of $G$ admits a Levi decomposition. As a consequence, there exists a regular open subgroup of $G$ which contains $G_u$.

Published
2021

10. Tempered homogeneous spaces IV

Author

Benoist, Yves and Kobayashi, Toshiyuki

Subjects
Mathematics - Group Theory, Mathematics - Representation Theory
Abstract

Let G be a complex semisimple Lie group and H a complex closed connected subgroup. Let g and h be their Lie algebras. We prove that the regular representation of G in $L^2(G/H)$ is tempered if and only if the orthogonal of h in g contains regular elements.

Published
2020

11. Harmonic quasi-isometric maps III :quotients of Hadamard manifolds

Author

Benoist, Yves and Hulin, Dominique

Subjects
Mathematics - Differential Geometry
Abstract

In a previous paper, we proved that a quasi-isometric map $f:X\longrightarrow Y$ between two pinched Hadamard manifolds $X$ and $Y$ is within bounded distance from a unique harmonic map. We extend this result to maps $f:\Gamma\backslash X\longrightarrow Y$, where $\Gamma$ is a convex cocompact discrete group of isometries of $X$ and $f$ is locally quasi-isometric at infinity.

Published
2020

12. Positive Harmonic Functions on the Heisenberg group I

Author

Benoist, Yves

Subjects
Mathematics - Group Theory, Mathematics - Probability
Abstract

We present the classification of positive harmonic functions on the Heisenberg group in the case of the southwest measure.

Published
2019

15. Arithmeticity of discrete subgroups containing horospherical lattices

Author

Benoist, Yves and Miquel, Sébastien

Subjects
Mathematics - Group Theory, 22E40
Abstract

Let $G$ be a semisimple real algebraic Lie group of real rank at least two and $U$ be the unipotent radical of a non-trivial parabolic subgroup. We prove that a discrete Zariski dense subgroup of $G$ that contains an irreducible lattice of $U$ is an arithmetic lattice of $G$. This solves a conjecture of Margulis and extends previous work of Hee Oh., Comment: 54 pages

Published
2018
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16. Geodesic planes in geometrically finite acylindrical 3-manifolds

Author

Benoist, Yves and Oh, Hee

Subjects
Mathematics - Dynamical Systems, Mathematics - Geometric Topology
Abstract

Let $M$ be a geometrically finite acylindrical hyperbolic 3-manifold and let $M^*$ denote the interior of the convex core of M. We show that any geodesic plane in $M^*$ is either closed or dense, and that there are only countably many closed geodesic planes in $M^*$. These results were obtained earlier by McMullen, Mohammadi, and the second named author when M is convex cocompact. As a corollary we obtain that when $M$ covers an arithmetic hyperbolic 3-manifold $M_0$, the topological behavior of a geodesic plane in $M^*$ is governed by that of the corresponding plane in $M_0$. We construct a counterexample of this phenomenon when $M_0$ is non-arithmetic., Comment: 39 pages

Published
2018

17. Tempered homogeneous spaces II

Author

Benoist, Yves and Kobayashi, Toshiyuki

Subjects
Mathematics - Representation Theory, Primary 22E46, Secondary 43A85, 22F30
Abstract

Let $G$ be a semisimple real Lie group with finite center and $H$ a connected closed subgroup. We establish a geometric criterion which detects whether the representation of $G$ in $L^2(G/H)$ is tempered., Comment: 34 pages. To be published in: Dynamics, Geometry, Number Theory: The Impact of Margulis on Modern Mathematics (eds. D. Fisher, D. Kleinbock, and G. Soifer), The University of Chicago Press

Published
2017

18. Recurrence on Affine Grassmannians

Author

Benoist, Yves and Bruère, Caroline

Subjects
Mathematics - Dynamical Systems, 22E40, 60J20
Abstract

We study the action of the affine group $G$ of $\mathbb{R}^d$ on the space $X_{k,\,d}$ of $k$-dimensional affine subspaces. Given a compactly-supported Zariski dense probability measure $\mu$ on $G$, we show that $X_{k,\,d}$ supports a $\mu$-stationary measure $\nu$ if and only if the $(k\!+\!1)^{\rm th}$-Lyapunov exponent of $\mu$ is strictly negative. In particular, when $\mu$ is symmetric, $\nu$ exists if and only if $2k\geq d$.

Published
2017
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19. Harmonic quasi-isometric maps II : negatively curved manifolds

Author

Benoist, Yves and Hulin, Dominique

Subjects
Mathematics - Differential Geometry, 53C43, 53C24, 53C35, 58E20
Abstract

We prove that a quasi-isometric map, and more generally a coarse embedding, between pinched Hadamard manifolds is within bounded distance from a unique harmonic map., Comment: 58 pages: in this version 2, two chapters on coarse embeddings have been added

Published
2017

20. Central limit theorem for linear groups

Author

Benoist, Yves and Quint, Jean-François

Subjects
Mathematics - Probability
Abstract

We prove a central limit theorem for random walks with finite variance on linear groups., Comment: Published at http://dx.doi.org/10.1214/15-AOP1002 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Published
2016
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21. Quasiisometric harmonic maps between rank one symmetric spaces

Author

Benoist, Yves and Hulin, Dominique

Subjects
Mathematics - Differential Geometry, 53C43 (Primary), 53C24, 53C35, 58E20 (Secondary)
Abstract

We prove that a quasiisometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture., Comment: 23 pages, 1 figure

Published
2015

23. A spectral gap theorem in simple Lie groups

Author

Benoist, Yves and de Saxcé, Nicolas

Subjects
Mathematics - Representation Theory, Mathematics - Group Theory
Abstract

We establish the spectral gap property for dense subgroups generated by algebraic elements in any compact simple Lie group, generalizing earlier results of Bourgain and Gamburd for unitary groups., Comment: 20 pages

Published
2014

24. Temperedness of reductive homogeneous spaces

Author

Benoist, Yves and Kobayashi, Toshiyuki

Subjects
Mathematics - Representation Theory, Mathematics - Functional Analysis, Primary 22E46, Secondary 43A85, 22F30
Abstract

Let G be a semisimple algebraic Lie group and H a reductive subgroup. We find geometrically the best even integer p for which the representation of G in L^2(G/H) is almost L^{p}. As an application, we give a criterion which detects whether this representation is tempered., Comment: to appear in Journal of European Mathematical Society

Published
2012
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25. The Local Limit Theorem for Products of Random Matrices

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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26. Zariski Dense Subsemigroups

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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27. Limit Laws for Products of Random Matrices

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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28. The Jordan Projection of Semigroups

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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29. The Local Limit Theorem for Cocycles

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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30. The Spectrum of the Complex Transfer Operator

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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31. Limit Laws for Cocycles

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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32. Regularity of the Stationary Measure

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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33. Transfer Operators over Contracting Actions

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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34. Random Walks on Reductive Groups

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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35. Loxodromic Elements

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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36. Reductive Groups and Their Representations

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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37. The Law of Large Numbers

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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38. Finite Index Subsemigroups

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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39. Linear Random Walks

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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40. Stationary Measures

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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41. Introduction

Author

Benoist, Yves, Quint, Jean-François, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Benoist, Yves, and Quint, Jean-François

Published
2016
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43. Effective equidistribution of S-integral points on symmetric varieties

Author

Benoist, Yves and Oh, Hee

Subjects
Mathematics - Number Theory, Mathematics - Metric Geometry, 14G05, 11F06, 22E40
Abstract

Let K be a global field of characteristic not 2. Let Z be a symmetric variety defined over K and S a finite set of places of K. We obtain counting and equidistribution results for the S-integral points of Z. Our results are effective when K is a number field., Comment: 46 pages

Published
2007

44. Polar decomposition for p-adic symmetric spaces

Author

Benoist, Yves and Oh, Hee

Subjects
Mathematics - Group Theory, Mathematics - Number Theory, 20G25
Abstract

Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution s of G. We prove a polar decomposition G=KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of the groups of k-points of maximal (k,s)-split tori, one for each H-conjugacy class. This decomposition is analogous to the well-known polar decomposition G=KAH for a real symmetric space G/H., Comment: 16 pages

Published
2006

45. Convolution and Square in Abelian Groups I

Author

Benoist, Yves

Subjects
Mathematics - Number Theory, General Mathematics, FOS: Mathematics, Number Theory (math.NT)
Abstract

We prove that on the cyclic groups of odd order d, there exist non zero functions whose convolution square f*f(2t) is proportional to their square f(t)^2 when the proportionality constant is given by an imaginary quadratic integer of norm d which is equal to 1 modulo 2. The proof involves theta functions on elliptic curves with complex multiplication.

Published
2023

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