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Diskr. Mat., 2017, Volume 29, Issue 2, Pages 84–95 (Mi dm1431)  

On Stone's renewal theorem for arithmetic distributions

M. S. Sgibnev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The well-known Stone's renewal theorem is refined for the case of arithmetic distributions having at least one exponentially decreasing tail. A very general version of the renewal theorem for arithmetic distributions with a semi-multiplicative bound of the residual term is proved.

Keywords: renewal theorem, Stone's theorem, arithmetic distribution, semimultiplicative sequence.

DOI: https://doi.org/10.4213/dm1431

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English version:
Discrete Mathematics and Applications, 2018, 28:6, 397–404

Bibliographic databases:

UDC: 519.218.4
Received: 21.12.2016

Citation: M. S. Sgibnev, “On Stone's renewal theorem for arithmetic distributions”, Diskr. Mat., 29:2 (2017), 84–95; Discrete Math. Appl., 28:6 (2018), 397–404

Citation in format AMSBIB
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