Sharpenings of Li's criterion for the Riemann hypothesis

DOI10.1007/s11040-005-9002-8zbMath1181.11055arXivmath/0506326OpenAlexW3104945120MaRDI QIDQ2432018

André Voros

Publication date: 25 October 2006

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506326

zbMATH Keywords

Riemann zeta functionStieltjes constantsRiemann hypothesissaddle-point methodLi's criterion

Mathematics Subject Classification ID

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

Related Items (19)

Li's criterion and the Riemann hypothesis for function fields ⋮ On asymptotic behavior of generalized Li coefficients in the Selberg class ⋮ Superzeta functions on function fields ⋮ Asymptotics of Keiper-Li coefficients ⋮ On asymptotic behavior of generalized Li coefficients ⋮ On certain sums over the non-trivial zeta zeroes ⋮ On the asymptotic criterion for the zero-free regions of certain $L$-functions ⋮ On differences of zeta values ⋮ Li coefficients for automorphic \(L\)-functions ⋮ On the discretized Li coefficients for a certain class of \(L\)-functions ⋮ ON INTERPOLATION FUNCTIONS FOR GENERALIZED Li COEFFICIENTS IN THE SELBERG CLASS ⋮ Evaluation of the Li coefficients on function fields and applications ⋮ On Li's criterion for the Riemann hypothesis for the Selberg class ⋮ The Li criterion and the Riemann hypothesis for the Selberg class. II ⋮ On Li's coefficients for the Rankin-Selberg \(L\)-functions ⋮ Explicit zero-free regions and a $\tau$-Li-type criterion ⋮ Discretized Keiper/Li Approach to the Riemann Hypothesis ⋮ On the Generalized Li’s Criterion Equivalent to the Riemann Hypothesis and Its First Applications ⋮ On the modified Li criterion for a certain class of \(L\)-functions

Cites Work

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• An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials
• Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions
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