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In [2] , it was conjectured that a particular shifted sum of even divisor sums vanishes, and in [11] , a formal argument was given for this vanishing. Shifted convolution sums of this form appear when computing the Fourier expansion of coefficients for the low energy scattering amplitudes in type IIB string theory [7] and have applications to subconvexity bounds of L -functions. In this article, we generalize the argument from [11] and rigorously evaluate shifted convolution of the divisor functions of the form ∑ n 1 , n 2 ∈ Z ∖ { 0 } n 1 + n 2 = n σ r 1 (n 1) σ r 2 (n 2) | n 1 | P and ∑ n 1 , n 2 ∈ Z ∖ { 0 } n 1 + n 2 = n σ r 1 (n 1) σ r 2 (n 2) | n 1 | Q log ⁡ | n 1 | where σ ν (n) = ∑ d | n d ν. In doing so, we derive exact identities for these sums and conjecture that particular sums similar to but different from the one found in [2] will also vanish. [ABSTRACT FROM AUTHOR]

We show that the values of elliptic Dedekind sums, after normalization, are equidistributed mod 1. The key ingredient is a non-trivial bound on generalized Selberg–Kloosterman sums for discrete subgroups of PSL 2 (C) using Poincaré series. [ABSTRACT FROM AUTHOR]

We correct an error found in Section 3.4.1 of Linear operators, the Hurwitz zeta function and Dirichlet L-functions published in JNT 217 (2020) 422–442. The error is related to the convergence of the inverse operator G − 1 defined in Section 3.3 and affects the statement and proof of Proposition 17. We provide a revised statement and proof. [ABSTRACT FROM AUTHOR]

At the 1900 International Congress of Mathematicians, Hilbert claimed that the Riemann zeta function is not the solution of any algebraic ordinary differential equation its region of analyticity [5]. In 2015, Van Gorder addresses the question of whether the Riemann zeta function satisfies a non -algebraic differential equation and constructs a differential equation of infinite order which zeta satisfies [7]. However, as he notes in the paper, this representation is formal and Van Gorder does not attempt to claim a region or type of convergence. In this paper, we show that Van Gorder's operator applied to the zeta function does not converge pointwise at any point in the complex plane. We also investigate the accuracy of truncations of Van Gorder's operator applied to the zeta function and show that a similar operator applied to zeta and other L -functions does converge. [ABSTRACT FROM AUTHOR]

We detail our experience running an annual four-day workshop at the University of Minnesota, called the Mathematics Project at Minnesota (MPM). The workshop is for undergraduates who come from groups underrepresented in mathematics and aims to increase the participation and success of such groups in the mathematics major at the University. In this paper, we explain how MPM is organized, discuss its objectives, and highlight some of the sessions that we feel are emblematic of the program's success. The paper concludes with an analysis of achievements and obstacles in the programs' first three years. [ABSTRACT FROM AUTHOR]