Perturbation of zeros of the Selberg zeta-function for $Γ_0(4)$

Roelof Bruggeman; Markus Fraczek; Dieter Mayer

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arXiv · 1201.2324

Perturbation of zeros of the Selberg zeta-function for $Γ_0(4)$

Roelof Bruggeman·Markus Fraczek·Dieter Mayer

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Abstract

We study the asymptotic behavior of zeros of the Selberg zeta-function for the congruence subgroup $Γ_0(4)$ as a function of a one-parameter family of characters tending to the trivial character. The motivation for the study comes from observations based on numerical computations. Some of the observed phenomena lead to precise theorems that we prove and compare with the original numerical results.

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Roelof Bruggeman, Markus Fraczek, Dieter Mayer. 2012-01-11. Perturbation of zeros of the Selberg zeta-function for $Γ_0(4)$. https://arxiv.org/abs/1201.2324

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