2 citations · 3 across the 10 of their papers we have counts for
10 papers
Convolution identities for complex-indexed divisor functions and modular graph functions
Ksenia Fedosova, Kim Klinger-Logan
We find exact identities for sums of the form \begin{equation*}\label{eq:convsumabs} \sum_{\stackrel{n_1+n_2 = n}{n_1 \in \mathbb{Z} \setminus \{ 0, n \} }} Q(n_1,n_2) σ_{-r_1}(n_1…
A Dedekind-Rademacher cocycle for Bianchi groups
Kim Klinger-Logan, Kalani Thalagoda, Tian An Wong
We construct a generalization of the Dedekind-Rademacher cocycle to congruence subgroups of , and derive some of its basic properties. In particular, we s…
The equidistribution of Elliptic Dedekind sums and generalized Selberg-Kloosterman sums
Kim Klinger-Logan, Tian An Wong
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…
Convolution identities for divisor sums and modular forms
Ksenia Fedosova, Kim Klinger-Logan, Danylo Radchenko
We prove exact identities for convolution sums of divisor functions of the form where $φ(…
Shifted convolution sums motivated by string theory
Kim Klinger-Logan, Ksenia Fedosova
In \cite{CGPWW2021}, it was conjectured that a particular shifted sum of even divisor sums vanishes, and in \cite{SDK}, a formal argument was given for this vanishing. Shifted conv…
The interaction as a Poincaré series, and a related shifted convolution sum
Kim Klinger-Logan, Stephen D. Miller, Danylo Radchenko
We complete the program, initiated in a 2015 paper of Green, Miller, and Vanhove, of directly constructing the automorphic solution to the string theory differential equa…
Whittaker Fourier type solutions to differential equations arising from string theory
Ksenia Fedosova, Kim Klinger-Logan
In this article, we find the full Fourier expansion for the generalized non-holomorphic Eisenstein series for certain values of parameters. We give a connection of the boundary con…
Linear Operators, the Hurwitz Zeta Function and Dirichlet -Functions
Bernardo Bianco Prado, Kim Klinger-Logan
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…
Differential equations in automorphic forms
Kim Klinger-Logan
Physicists such as Green, Vanhove, et al show that differential equations involving automorphic forms govern the behavior of gravitons. One particular point of interest is solution…
A spectral interpretation of zeros of certain functions
Kim Klinger-Logan
We prove that all the zeros of certain meromorphic functions are on the critical line , and are simple (except possibly when ). We prove this by relating t…