Some sums over the non-trivial zeros of the Riemann zeta function

Jesús Guillera

Published 2013-07-22, updated 2014-06-19Version 7

We prove some identities, which involve the non-trivial zeros of the Riemann zeta function. From them we derive some convergent asymptotic expansions related to the work by Cram\'er, and also new representations for some arithmetical functions in terms of the non-trivial zeros.