Chebyshev estimates for Beurling generalized prime numbers. I.

DOI10.1016/J.JNT.2012.04.019zbMath1266.11109arXiv1201.1405OpenAlexW2098490266MaRDI QIDQ448225

Jasson Vindas

Publication date: 30 August 2012

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

Full work available at URL: https://arxiv.org/abs/1201.1405

zbMATH Keywords

abstract prime number theoryarithmetic semigroupsBeurling primesChebyshev's inequalities

Mathematics Subject Classification ID

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

Related Items (2)

Extensions of Beurling's prime number theorem ⋮ Density estimates for the zeros of the Beurling ζ function in the critical strip

Cites Work

• 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 set of generalized numbers showing Beurling's theorem to be sharp
• The prime number theorem for Beurling's generalized numbers. New cases
• Chebyshev Estimates for Beurling Generalized Prime Numbers
• Chebyshev Type Estimates for Beurling Generalized Prime Numbers
• Chebyshev Type Estimates for Beurling Generalized Prime Numbers. II
• Tauberian Theory
• Beurling Generalized Prime Number Systems in Which the Chebyshev Inequalities Fail
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