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Perturbation of zeros of the Selberg zeta function for \(\Gamma_0(4)\). (English) Zbl 1302.11062

Summary: We study the asymptotic behavior of zeros of the Selberg zeta function for the congruence subgroup \(\Gamma_0(4)\) 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, which we prove and compare with the original numerical results.

MSC:

11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)
11F72 Spectral theory; trace formulas (e.g., that of Selberg)
37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.

Citations:

Zbl 1252.11068

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References:

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