Beurling Generalized Numbers

DOI10.1090/surv/213zbMath1378.11002OpenAlexW2546823084MaRDI QIDQ2829451

Harold G. Diamond, Wen-Bin Zhang

Publication date: 28 October 2016

Published in: Mathematical Surveys and Monographs (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/surv/213

zbMATH Keywords

generalized primesBeurling numbersChebyshev boundsgeneralized integersDickman and Buchstab functionsgeneralized numbers, g-numbersWiener-Ikehara Tauberian theorems

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Other Dirichlet series and zeta functions (11M41) Distribution of primes (11N05) Generalized primes and integers (11N80)

Related Items (18)

On PNT equivalences for Beurling numbers ⋮ On zero-density estimates and the PNT in short intervals for Beurling generalized numbers ⋮ Beurling integers with RH and large oscillation ⋮ Multiplicative functions with sum zero over Beurling generalized prime number systems ⋮ Density estimates for the zeros of the Beurling ζ function in the critical strip ⋮ Spectral asymptotics for a family of LCM matrices ⋮ ${\varOmega }$-result for the remainder term in Beurling’s prime number theorem for well-behaved integers ⋮ THE OPTIMAL MALLIAVIN-TYPE REMAINDER FOR BEURLING GENERALIZED INTEGERS ⋮ The average order of the Möbius function for Beurling primes ⋮ Like\(\mathbb{N}\)'s -- a point of view on natural numbers ⋮ PRIME NUMBER THEOREM EQUIVALENCES AND NON‐EQUIVALENCES ⋮ Completely multiplicative functions with sum zero over generalised prime systems ⋮ Halász's theorem for Beurling generalized numbers ⋮ Note on a conjecture of Bateman and diamond concerning the abstract PNT with Malliavin-type remainder ⋮ On Diamond's \(L^1\) criterion for asymptotic density of Beurling generalized integers ⋮ M(x)=o(x) Estimates for Beurling numbers ⋮ Arithmetic functions of higher-order primes ⋮ Beurling numbers whose number of prime factors lies in a specified residue class

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