Some questions of connection between summation functions and the corresponding Dirichlet series
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910407257489408 |
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| author | Volfson, Victor |
| author_facet | Volfson, Victor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some questions of connection between summation functions and the corresponding Dirichlet series Volfson, Victor General Mathematics 11N37 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. |
| title | Some questions of connection between summation functions and the corresponding Dirichlet series |
| topic | General Mathematics 11N37 |
| url | https://arxiv.org/abs/2404.08012 |