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arXiv · 2302.02844

Dirichlet series associated to representation numbers of ideals in real quadratic number fields

Johannes J. Buck
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Abstract

In this rather computational paper, we determine certain representation numbers of ideals in real quadratic number fields explicitly in order to obtain a representation of the associated Dirichlet series in terms of Dirichlet L-functions and a generalized divisor sum. A direct and important consequence is that the Dirichlet series has a meromorphic continuation to the whole complex plane and a simple pole at $s=2$ whose residue can be made explicit in terms of the Dirichlet L-functions and the generalized divisor sum.

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Johannes J. Buck. 2023-02-06. Dirichlet series associated to representation numbers of ideals in real quadratic number fields. https://arxiv.org/abs/2302.02844

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