Hardy-Littlewood-Riesz type equivalent criteria for the generalized Riemann hypothesis

DOI10.1007/s00605-023-01857-8arXiv2208.07596OpenAlexW4366402923WikidataQ121932825 ScholiaQ121932825MaRDI QIDQ6097050

Meghali Garg, Bibekananda Maji

Publication date: 9 June 2023

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.07596

zbMATH Keywords

Riemann zeta functiongeneralized Riemann hypothesisDirichlet \(L\)-functionnon-trivial zerosequivalent criteria

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)

Cites Work

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• Character analogues of Ramanujan-type integrals involving the Riemann \(\Xi \)-function
• Riesz-type criteria and theta transformation analogues
• An exact formula for a Lambert series associated to a cusp form and the Möbius function
• A modular relation involving non-trivial zeros of the Dedekind zeta function, and the generalized Riemann hypothesis
• A sequential Riesz-like criterion for the Riemann Hypothesis
• Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms
• Criteria equivalent to the Riemann Hypothesis
• Riesz-type criteria for the Riemann hypothesis

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