Siddhi Pathak, Penn State University
"Convolution of values of the Lerch zeta-function"
Let $\zeta(s) := \sum_{n=1}^{\infty} n^{ -s }$ for $\Re(s) > 1$ denote the Riemann zeta-function. It is well known, due to Euler, that $ \zeta(2k) $ is a rational multiple of $ \pi^{ 2k }$. However, the nature of $\zeta( 2k+1 )$ remains a mystery. On adopting a wider perspective, the values $\zeta(n)$ seem intimately connected with the values of it's multi-variable analog at positive integers, namely, multi-zeta values (MZVs). MZVs satisfy a plethora of interesting identities and enjoy a rich algebraic structure. In this talk, we discuss a similar connection in the context of the Lerch zeta-function (an exponential twist of the Hurwitz zeta-function). This is joint work with M. Ram Murty.
MC 5417