Chebyshev estimates for Beurling generalized prime numbers

Author:
Harold G. Diamond

Journal:
Proc. Amer. Math. Soc. **39** (1973), 503-508

MSC:
Primary 10H20

DOI:
https://doi.org/10.1090/S0002-9939-1973-0314782-4

MathSciNet review:
0314782

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Abstract: We consider a Beurling generalized number system for which the counting function of the integers satisfies

**[1]**Paul T. Bateman and Harold G. Diamond,*Asymptotic distribution of Beurling’s generalized prime numbers*, Studies in Number Theory, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1969, pp. 152–210. MR**0242778****[2]**A. Beurling,*Analyse de la loi asymptotique de la distribution des nombres premiers généralisés*. I, Acta Math.**68**(1937), 255-291.**[3]**T. M. K. Davison,*A Tauberian theorem and analogues of the prime number theorem*, Canad. J. Math.**20**(1968), 362–367. MR**0224569**, https://doi.org/10.4153/CJM-1968-032-2**[4]**Harold G. Diamond,*Asymptotic distribution of Beurling’s generalized integers*, Illinois J. Math.**14**(1970), 12–28. MR**0252334****[5]**R. S. Hall,*Theorems about Beurling's generalized primes and the associated zeta function*, Ph.D. Thesis, University of Illinois, Urbana, Ill., 1967.**[6]**S. L. Segal,*A Tauberian theorem for Dirichlet convolutions*, Illinois J. Math.**13**(1969), 316–320. MR**0238779**

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0314782-4

Article copyright:
© Copyright 1973
American Mathematical Society