On zero-density estimates and the PNT in short intervals for Beurling generalized numbers

DOI10.4064/aa221223-15-2arXiv2211.08716OpenAlexW4365131379MaRDI QIDQ6045525

Frederik Broucke, Gregory Debruyne

Publication date: 31 May 2023

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.08716

zbMATH Keywords

Riemann zeta functionzero-density estimateslarge values estimategeneralized Dirichlet polynomialBeurling generalized prime number systemsmean value theorem for Dirichlet polynomialsPNT in short intervalswell-behaved integerszero detection method

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)

Cites Work

• Beurling primes with large oscillation
• Topics in multiplicative number theory
• Beurling Generalized Numbers
• Some extremal functions in Fourier analysis
• A Riemann–von Mangoldt-Type Formula for the Distribution of Beurling Primes
• On the difference between consecutive primes
• Density estimates for the zeros of the Beurling ζ function in the critical strip
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