Notes on the Riemann zeta-function. I

DOI10.1006/aima.1998.1760zbMath0920.11062OpenAlexW1965428540MaRDI QIDQ1273840

Eric Saias, Michel Balazard

Publication date: 30 March 1999

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.1998.1760

zbMATH Keywords

Möbius functionconvergence of special sequencesnonvanishing of the Riemann zeta function

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (9)

Notes on the Riemann \(\zeta\)-function. IV ⋮ An approach of generalised Riemann hypothesis through sequences ⋮ On a question of Balazard and Saias related to the Riemann hypothesis ⋮ Note on the Riemann \(\zeta\)-function. III ⋮ Fourier coefficients associated with the Riemann zeta-function ⋮ Beurling’s theorem, Davenport’s formula, and the Riemann hypothesis ⋮ Arithmetic and analysis of the series \(\sum_{n=1}^\infty \frac{1}{n} \sin \frac{x}{n}\) ⋮ Zeros of Dirichlet polynomials via a density criterion ⋮ Zero-free regions for Dirichlet series

Cites Work

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• A real variable restatement of Riemann's hypothesis
• On Beurling's real variable reformulation of the Riemann Hypothesis
• Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann \(\zeta\)-function
• Notes on the Theory and Application of Fourier Transforms. I-II
• A CLOSURE PROBLEM RELATED TO THE RIEMANN ZETA-FUNCTION

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