Koshliakov kernel and identities involving the Riemann zeta function

Atul Dixit; Nicolas Robles; Arindam Roy; Alexandru Zaharescu

paper

Koshliakov kernel and identities involving the Riemann zeta function

arXiv:1505.01552

Abstract

Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions $J_{z} (x), Y_{z} (x)$ and $K_{z} (x)$ are studied. Interesting special cases of these identities are derived, one of which is connected to a well-known transformation due to Ramanujan, and Guinand.

21 pages, 5 figures; submitted for publication