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

General Mathematics 2024-04-15 v1

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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Cite

@article{arxiv.2404.08012,
  title  = {Some questions of connection between summation functions and the corresponding Dirichlet series},
  author = {Victor Volfson},
  journal= {arXiv preprint arXiv:2404.08012},
  year   = {2024}
}

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13 pages