Illinois Journal of Mathematics

On zeros of the derivative of the three-dimensional Selberg zeta function

Makoto Minamide

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In this article, we study the distribution of zeros of the derivative of the Selberg zeta function for compact three-dimensional hyperbolic spaces. We obtain an asymptotic formula for the counting function of its zeros. This is a three-dimensional version of the celebrated work of Wenzhi Luo. We also deduce other asymptotic formulas relating to its zeros from the above formula.

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Illinois J. Math., Volume 52, Number 4 (2008), 1165-1182.

First available in Project Euclid: 18 November 2009

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Primary: 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas 11F72: Spectral theory; Selberg trace formula


Minamide, Makoto. On zeros of the derivative of the three-dimensional Selberg zeta function. Illinois J. Math. 52 (2008), no. 4, 1165--1182. doi:10.1215/ijm/1258554355.

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