The value-distribution of Artin $L$-functions associated with cubic fields in conductor aspect
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866912072717041664 |
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| author | Mine, Masahiro |
| author_facet | Mine, Masahiro |
| contents | Arising from the factorizations of Dedekind zeta-functions of cubic fields, we obtain Artin $L$-functions of certain two-dimensional representations. In this paper, we study the value-distribution of such Artin $L$-functions for families of non-Galois cubic fields in conductor aspect. We prove that various mean values of the Artin $L$-functions are represented by integrals involving a density function which can be explicitly constructed. By the class number formula, the result is applied to the study on the distribution of class numbers of cubic fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1905_11851 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The value-distribution of Artin $L$-functions associated with cubic fields in conductor aspect Mine, Masahiro Number Theory Primary 11R42, Secondary 11R16 Arising from the factorizations of Dedekind zeta-functions of cubic fields, we obtain Artin $L$-functions of certain two-dimensional representations. In this paper, we study the value-distribution of such Artin $L$-functions for families of non-Galois cubic fields in conductor aspect. We prove that various mean values of the Artin $L$-functions are represented by integrals involving a density function which can be explicitly constructed. By the class number formula, the result is applied to the study on the distribution of class numbers of cubic fields. |
| title | The value-distribution of Artin $L$-functions associated with cubic fields in conductor aspect |
| topic | Number Theory Primary 11R42, Secondary 11R16 |
| url | https://arxiv.org/abs/1905.11851 |