Wiener-Ikehara theorems and the Beurling generalized primes

DOI10.1007/S00605-013-0597-8zbMath1384.11090OpenAlexW2010894814MaRDI QIDQ403831

Wen-Bin Zhang

Publication date: 29 August 2014

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

Full work available at URL: https://doi.org/10.1007/s00605-013-0597-8

zbMATH Keywords

prime number theoremBeurling generalized primesChebyshev prime boundsWiener-Ikehara Tauberian theorem

Mathematics Subject Classification ID

Generalized primes and integers (11N80) Tauberian theorems (11M45)

Related Items (6)

On PNT equivalences for Beurling numbers ⋮ Extensions of Beurling's prime number theorem ⋮ Note on the absence of remainders in the Wiener-Ikehara theorem ⋮ Some examples in the theory of Beurling’s generalized prime numbers ⋮ Complex Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior ⋮ A proof of a conjecture of Bateman and Diamond on Beurling generalized primes

Cites Work

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• 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
• Chebyshev bounds for Beurling numbers
• Optimality of Chebyshev bounds for Beurling generalized numbers

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