# On certain sums over the nontrivial zeta zeros

## TL;DR

This paper investigates coefficients related to the Riemann zeta function's nontrivial zeros, providing new relations, representations, and asymptotic behavior under the Riemann hypothesis.

## Contribution

It introduces novel expressions and integral representations for coefficients linked to zeta zeros, advancing understanding of their properties and asymptotics.

## Key findings

- Expressed $b_n$ as sums over zeta zeros
- Derived integral representations of $b_n$
- Established asymptotic form $b_n o 2^{-n-2}
abla n$ under RH

## 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 $b_n \sim 2^{-n-2}\ln n$.