Remarks on number theory over additive arithmetical semigroups-Reference-Cited by-同舟云学术

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Remarks on number theory over additive arithmetical semigroups

Published:2020-03-28 Issue:3 Volume:72 Page:371-390
ISSN:1027-3190
Container-title:Ukrains’kyi Matematychnyi Zhurnal
language:
Short-container-title:Ukr. Mat. Zhurn.

Author:

Indlekofer K.-H.,Kaya E.

Abstract

UDC 511 We deal with additive arithmetical semigroups and present old and new proofs for the distribution of zeros of the corresponding ζ -functions. We use these results to prove prime number theorems and a Selberg formula for such semigroups.

Publisher

Institute of Mathematics National Academy of Sciences of Ukraine

Reference22 articles.

1. Barát, A.; Indlekofer, K.-H. On mean-value theorems for multiplicative functions in additive arithmetical semigroups. Ann. Univ. Sci. Budapest. Sect. Comput. 33 (2010), 49--72. MR2891033

2. Barát, Anna; Indlekofer, Karl-Heinz. Mean-value theorems for uniformly summable multiplicative functions on additive arithmetical semigroups. Ann. Univ. Sci. Budapest. Sect. Comput. 40 (2013), 105--122. MR3129159

3. Beurling, Arne. Analyse de la loi asymptotique de la distribution des nombres premiers généralisés. I. (French) Acta Math. 68 (1937), no. 1, 255--291. doi: 10.1007/BF02546666

4. Carlitz, L. The distribution of irreducible polynomials in several indeterminates. Illinois J. Math. 7 1963 371--375. MR0153665

5. Fogels, E. On the abstract theory of primes. I. Acta Arith. 10 (1964/65), 137--182. doi: 10.4064/aa-10-2-137-182

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