On certain sums over the non-trivial zeta zeroes

DOI10.1098/RSPA.2010.0064zbMath1247.11108arXiv0912.2390OpenAlexW2157244519MaRDI QIDQ2997313

Mark W. Coffey

Publication date: 6 May 2011

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.2390

zbMATH Keywords

integral representationRiemann zeta-functionRiemann hypothesisnon-trivial zerosLi/Keiper constants

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (2)

On the Li coefficients for the Hecke \(L\)-functions ⋮ On the Generalized Li’s Criterion Equivalent to the Riemann Hypothesis and Its First Applications

Cites Work

• Complements to Li's criterion for the Riemann Hypothesis
• The positivity of a sequence of numbers and the Riemann hypothesis
• Relations and positivity results for the derivatives of the Riemann \(\xi\) function.
• The theta-Laguerre calculus formulation of the Li/Keiper constants
• Sharpenings of Li's criterion for the Riemann hypothesis
• Toward verification of the Riemann hypothesis: application of the Li criterion
• An explicit formula and estimations for Hecke L-functions: Applying the Li criterion
• New results concerning power series expansions of the Riemann xi function and the Li/Keiper constants

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