Beurling integers with RH and large oscillation

DOI10.1016/j.aim.2020.107240zbMath1468.11184arXiv2004.11501OpenAlexW3018004991MaRDI QIDQ2189509

Gregory Debruyne, Jasson Vindas, Frederik Broucke

Publication date: 15 June 2020

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

Full work available at URL: https://arxiv.org/abs/2004.11501

zbMATH Keywords

saddle-point methodBeurling generalized prime numbersBohr's extremal example for convexity boundDiamond-Montgomery-Vorhauer probabilistic methodgeneralized integers with large oscillationgeneralized integers with Riemann hypothesis

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Distribution of primes (11N05) Generalized primes and integers (11N80)

Related Items (5)

Multiplicative functions with sum zero over Beurling generalized prime number systems ⋮ Density estimates for the zeros of the Beurling ζ function in the critical strip ⋮ THE OPTIMAL MALLIAVIN-TYPE REMAINDER FOR BEURLING GENERALIZED INTEGERS ⋮ Completely multiplicative functions with sum zero over generalised prime systems ⋮ Note on a conjecture of Bateman and diamond concerning the abstract PNT with Malliavin-type remainder

Cites Work

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• Diamond's version of the Dirichlet hyperbola method
• Asymptotic distribution of Beurling's generalized integers
• Beurling Generalized Numbers
• Some examples in the theory of Beurling’s generalized prime numbers
• An example in Beurling's theory of primes
• Asymptotic distribution of Beurling integers
• Examples of beurling prime systems

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