On certain sums over the nontrivial zeta zeros

Abstract

We study coefficients $b_n$ that are expressible as sums over the Li/Keiper constants $\lambda_j$. We present a number of relations for and representations of $b_n$. These include the expression of $b_n$ as a sum over nontrivial zeros of the Riemann zeta function, as well as integral representations. Conditional on the Riemann hypothesis, we provide the asymptotic form of $b_n \sim 2^{-n-2}\ln n$.