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arXiv · 1905.11851

The value-distribution of Artin $L$-functions associated with cubic fields in conductor aspect

Masahiro Mine
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Abstract

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.

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Masahiro Mine. 2019-05-28. The value-distribution of Artin $L$-functions associated with cubic fields in conductor aspect. https://doi.org/10.1007/s00209-023-03326-2

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