Illinois Journal of Mathematics

The $a$-points of the Selberg zeta-function are uniformly distributed modulo one

Ramūnas Garunkštis, Jörn Steuding, and Raivydas Šimėnas

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Let $Z(s)$ be the Selberg zeta-function associated with a compact Riemann surface. We prove that the imaginary parts of the nontrivial $a$-points of $Z(s)$ are uniformly distributed modulo one. We also consider the question whether the eigenvalues of the corresponding Laplacian are uniformly distributed modulo one.

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Illinois J. Math., Volume 58, Number 1 (2014), 207-218.

First available in Project Euclid: 1 April 2015

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Primary: 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas


Garunkštis, Ramūnas; Steuding, Jörn; Šimėnas, Raivydas. The $a$-points of the Selberg zeta-function are uniformly distributed modulo one. Illinois J. Math. 58 (2014), no. 1, 207--218. doi:10.1215/ijm/1427897174.

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