On a Mertens-type conjecture for number fields
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913648425828352 |
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| author | Hu, Daniel Kaneko, Ikuya Martin, Spencer Schildkraut, Carl |
| author_facet | Hu, Daniel Kaneko, Ikuya Martin, Spencer Schildkraut, Carl |
| contents | We introduce a number field analogue of the Mertens conjecture and demonstrate its falsity for all but finitely many number fields of any given degree. We establish the existence of a logarithmic limiting distribution for the analogous Mertens function, expanding upon work of Ng. Finally, we explore properties of the generalized Mertens function of certain dicyclic number fields as consequences of Artin factorization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_06665 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On a Mertens-type conjecture for number fields Hu, Daniel Kaneko, Ikuya Martin, Spencer Schildkraut, Carl Number Theory 11N56 (Primary), 11N64 (Secondary) We introduce a number field analogue of the Mertens conjecture and demonstrate its falsity for all but finitely many number fields of any given degree. We establish the existence of a logarithmic limiting distribution for the analogous Mertens function, expanding upon work of Ng. Finally, we explore properties of the generalized Mertens function of certain dicyclic number fields as consequences of Artin factorization. |
| title | On a Mertens-type conjecture for number fields |
| topic | Number Theory 11N56 (Primary), 11N64 (Secondary) |
| url | https://arxiv.org/abs/2109.06665 |