On Beurling's generalized prime numbers. Proof of a conjecture of Bateman and Diamond

DOI10.5802/JTNB.201zbMath0905.11042OpenAlexW2314581586WikidataQ122905579 ScholiaQ122905579MaRDI QIDQ1388985

Jean-Pierre Kahane

Publication date: 21 January 1999

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1997__9_2_251_0

zbMATH Keywords

Wiener algebraBeurling algebraSobolev algebrageneralized prime numbers

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Generalized primes and integers (11N80)

Related Items (10)

Conditions for Beurling numbers to have a density ⋮ Extensions of Beurling's prime number theorem ⋮ Wiener-Ikehara theorems and the Beurling generalized primes ⋮ Density estimates for the zeros of the Beurling ζ function in the critical strip ⋮ On General Prime Number Theorems with Remainder ⋮ Chebyshev estimates for Beurling generalized prime numbers. I. ⋮ On Diamond's \(L^1\) criterion for asymptotic density of Beurling generalized integers ⋮ 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 ⋮ An example in Beurling's theory of generalised primes ⋮ A proof of a conjecture of Bateman and Diamond on Beurling generalized primes

Cites Work

• The prime number theorem for Beurling's generalized numbers
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