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

20 pages, 1 figure

References in corpus (3)

• Toward verification of the Riemann hypothesis: Application of the Li criterion
• Sharpenings of Li's criterion for the Riemann Hypothesis
• Eigenvalue Density, Li's Positivity, and the Critical Strip

Cited by in corpus (5)

• Will a physicist prove the Riemann Hypothesis?
• First applications of generalized Li's criterion to study the Riemann zeta-function zeroes location
• Asymptotic of the generalized Li's sums which non-negativity is equivalent to the Riemann Hypothesis
• Generating functions for the generalized Li's sums
• Reformulation of the Li criterion for the Selberg class