On the Li coefficients for the Hecke \(L\)-functions

DOI10.1007/s11040-014-9141-xzbMath1356.11060OpenAlexW2058769520MaRDI QIDQ471812

Kamel Mazhouda, Raouf Ouni, Sami Omar

Publication date: 17 November 2014

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

Full work available at URL: https://doi.org/10.1007/s11040-014-9141-x

zbMATH Keywords

Riemann hypothesisHecke \(L\)-functionsLi's criterion

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (9)

Li's criterion and the Riemann hypothesis for function fields. II. ⋮ A computational approach to the generalized Riemann hypothesis ⋮ On a class of Epstein zeta functions ⋮ Li's criterion for Epstein zeta functions, generalization of Kronecker's limit formula and the Gauss problem ⋮ On the discretized Li coefficients for a certain class of \(L\)-functions ⋮ On relations equivalent to the generalized Riemann hypothesis for the Selberg class ⋮ On a generalization of Kronecker's limit formula ⋮ A note on Li’s coefficients for Hecke L-functions ⋮ On the modified Li criterion for a certain class of \(L\)-functions

Uses Software

• PARI/GP
• SageMath

Cites Work

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• Complements to Li's criterion for the Riemann Hypothesis
• The positivity of a sequence of numbers and the Riemann hypothesis
• Explicit formulas for Dirichlet and Hecke \(L\)-functions
• Li coefficients for automorphic \(L\)-functions
• Toward verification of the Riemann hypothesis: application of the Li criterion
• Li's criterion and zero-free regions of \(L\)-functions
• On certain sums over the non-trivial zeta zeroes
• On the zeros of Dirichlet -functions
• An explicit formula and estimations for Hecke L-functions: Applying the Li criterion
• Bounded nonvanishing functions and bateman functions
• Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝

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