Some questions of connection between summation functions and the corresponding Dirichlet series

Victor Volfson

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arXiv · 2404.08012

Some questions of connection between summation functions and the corresponding Dirichlet series

Victor Volfson

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Abstract

The paper proves a generalization of Wintner's theorem on the asymptotics of summation functions to the case of summation functions with nonlinear asymptotics. The class of arithmetic functions that have a logarithmic asymptotic mean is studied. The Kronecker lemma is generalized to the case when the corresponding Dirichlet series diverges. Several assertions are proven and illustrative examples are given.

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Victor Volfson. 2024-04-10. Some questions of connection between summation functions and the corresponding Dirichlet series. https://arxiv.org/abs/2404.08012

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