Extensions of Beurling's prime number theorem

DOI10.1142/S1793042115400126zbMath1337.11068OpenAlexW2128654391MaRDI QIDQ2942529

Wen-Bin Zhang

Publication date: 11 September 2015

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042115400126

zbMATH Keywords

Fourier transformprime number theoremPoisson summation formulaBeurling generalized primesSchwartz functionChebyshev boundsextended Wiener-Ikehara Tauberian theorem

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 (4)

Density estimates for the zeros of the Beurling ζ function in the critical strip ⋮ On General Prime Number Theorems with Remainder ⋮ On Diamond's \(L^1\) criterion for asymptotic density of Beurling generalized integers ⋮ Asymptotic distribution of Beurling integers

Cites Work

• Wiener-Ikehara theorems and the Beurling generalized primes
• Chebyshev estimates for Beurling generalized prime numbers. I.
• 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
• A proof of a conjecture of Bateman and Diamond on Beurling generalized primes
• The prime number theorem for Beurling's generalized numbers
• Analyse de la loi asymptotique de la distribution des nombres premiers généralises
• Chebyshev bounds for Beurling numbers
• Optimality of Chebyshev bounds for Beurling generalized numbers

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