A proof of a conjecture of Bateman and Diamond on Beurling generalized primes

DOI10.1007/s00605-014-0681-8zbMath1321.11107OpenAlexW1986029412WikidataQ123200725 ScholiaQ123200725MaRDI QIDQ2339373

Wen-Bin Zhang

Publication date: 31 March 2015

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

Full work available at URL: https://doi.org/10.1007/s00605-014-0681-8

zbMATH Keywords

Fourier transformprime number theoremPoisson summation formulaBeurling generalized primesWiener-Ikehara Tauberian theoremSchwartz function

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Generalized primes and integers (11N80) Tauberian theorems (11M45)

Related Items (3)

Extensions of Beurling's prime number theorem ⋮ Density estimates for the zeros of the Beurling ζ function in the critical strip ⋮ Some examples in the theory of Beurling’s generalized prime numbers

Cites Work

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• Wiener-Ikehara theorems and the Beurling generalized primes
• The role of Wiener's, Beurling's and Sobolev's algebras \(A\), \(A^\infty\) and \(H^1\) in the theory of Beurling's generalized prime numbers
• On Beurling's generalized prime numbers. Proof of a conjecture of Bateman and Diamond
• The prime number theorem for Beurling's generalized numbers
• A set of generalized numbers showing Beurling's theorem to be sharp
• The prime number theorem for Beurling's generalized numbers. New cases

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