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Probabilistic Number Theory in Additive Arithmetic Semigroups, III

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Abstract

We extend the investigation of quantitative mean-value theorems of completely multiplicative functions on additive arithmetic semigroups given in our previous paper. Then the new and old quantitative mean-value theorems are applied to the investigation of local distribution of values of a special additive function Ω*(a). The result is unexpected from the point of view of classical number theory. This reveals the fact that the essential divergence of the theory of additive arithmetic semigroups from classical number theory is not related to the existence of a zero of the zeta function Z(y) at y = −q −1.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois, 61801, USA;

    Wen-Bin Zhang

  2. Department of Mathematics, South China University of Technology, Guangzhou, People's Republic of China

    Wen-Bin Zhang

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  1. Wen-Bin Zhang
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Zhang, WB. Probabilistic Number Theory in Additive Arithmetic Semigroups, III. The Ramanujan Journal 6, 387–428 (2002). https://doi.org/10.1023/A:1021108332595

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