On certain sums over the non-trivial zeta zeroes

Abstract

We study coefficients b n , expressible as sums over the Li/Keiper constants λ j , that contain information on the Riemann xi function. We present a number of relations for and representations of b n . These include the expression of b n as a sum over non-trivial zeroes of the Riemann zeta function, as well as integral representations. Conditional on the Riemann hypothesis, we provide the asymptotic form of .