Illinois Journal of Mathematics

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

Makoto Minamide

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 18 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258554355

Digital Object Identifier
doi:10.1215/ijm/1258554355

Mathematical Reviews number (MathSciNet)
MR2595760

Zentralblatt MATH identifier
1204.11148

Subjects
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

Citation

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. https://projecteuclid.org/euclid.ijm/1258554355


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