Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Number Theory Seminar


Wednesday, May 8th, 2019

Time: 3:30-4:30 p.m.  Place: Jeffery Hall 110

Speaker: Siddhi Pathak (Queen's University)

Title: Convolution sums of values of the Lerch zeta-function

Abstract: In 1887, Lerch introduced the function, $\Phi(z, \alpha, s) := \sum_{n=0}^{\infty} \frac{ z^n } { {(n + \alpha)}^s },$ for $|z| = 1$, $0 < \alpha \leq 1$ and $\Re(s)>1$. This function is a generalization of the Riemann zeta-function, the Hurwitz zeta-functions as well as the polylogarithms. In this talk, we discuss convolution sum identities of values of the Lerch zeta-function at positive integers. This study is inspired by similar identities for values of the Riemann zeta-function, which were known to Euler, and leads one naturally into the realm of multiple Hurwitz zeta-functions. This is joint work with Prof. M. Ram Murty.