Some examples in the theory of Beurling’s generalized prime numbers

DOI10.4064/aa8168-7-2016zbMath1377.11108arXiv1505.04174OpenAlexW2096435532WikidataQ114022064 ScholiaQ114022064MaRDI QIDQ2833610

Gregory Debruyne, Jasson Vindas, Jan-Christoph Schlage-Puchta

Publication date: 18 November 2016

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

Full work available at URL: https://arxiv.org/abs/1505.04174

zbMATH Keywords

prime number theoremBeurling generalized integersBeurling generalized primes

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Distribution of primes (11N05) Generalized primes and integers (11N80) Tauberian theorems (11M45)

Related Items (7)

On PNT equivalences for Beurling numbers ⋮ Beurling integers with RH and large oscillation ⋮ Density estimates for the zeros of the Beurling ζ function in the critical strip ⋮ On General Prime Number Theorems with Remainder ⋮ An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions ⋮ On powers of the compositions involving Dirac-delta and infinitely differentiable functions ⋮ M(x)=o(x) Estimates for Beurling numbers

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• A set of generalized numbers showing Beurling's theorem to be sharp
• The prime number theorem for Beurling's generalized numbers. New cases
• Two results on Beurling generalized numbers
• The structure of quasiasymptotics of Schwartz distributions
• Structural theorems for quasiasymptotics of distributions at infinity

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