On universality of general Dirichlet series
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913268472217600 |
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| author | Bayart, Frédéric Kouroupis, Athanasios |
| author_facet | Bayart, Frédéric Kouroupis, Athanasios |
| contents | In the present work, we establish sufficient conditions for a Dirichlet series induced by general frequencies to be universal with respect to vertical translations. Our results can be applied to known universal objects such as Hurwitz zeta functions and also can provide new examples of universal Dirichlet series including the alternating prime zeta function $\sum_{n\geq1}(-1)^np_n^{-s}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On universality of general Dirichlet series Bayart, Frédéric Kouroupis, Athanasios Complex Variables Number Theory 30K10 In the present work, we establish sufficient conditions for a Dirichlet series induced by general frequencies to be universal with respect to vertical translations. Our results can be applied to known universal objects such as Hurwitz zeta functions and also can provide new examples of universal Dirichlet series including the alternating prime zeta function $\sum_{n\geq1}(-1)^np_n^{-s}$. |
| title | On universality of general Dirichlet series |
| topic | Complex Variables Number Theory 30K10 |
| url | https://arxiv.org/abs/2402.00656 |