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Zeros of the Selberg zeta function for symmetric infinite area hyperbolic surfaces
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Pollicott, Mark and Vytnova, Polina (2019) Zeros of the Selberg zeta function for symmetric infinite area hyperbolic surfaces. Geometriae Dedicata, 201 . pp. 155-186. doi:10.1007/s10711-018-0386-6 ISSN 0046-5755.
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Official URL: http://dx.doi.org/10.1007/s10711-018-0386-6
Abstract
In the present paper we give a simple mathematical foundation for describing the zeros of the Selberg zeta functions ZX for certain very symmetric infinite area surfaces X. For definiteness, we consider the case of three funneled surfaces. We show that the zeta function is a complex almost periodic function which can be approximated by complex trigonometric polynomials on large domains (in Theorem 4.2). As our main application, we provide an explanation of the striking empirical results of Borthwick (Exp Math 23(1):25–45, 2014) (in Theorem 1.5) in terms of convergence of the affinely scaled zero sets to standard curves ℓ
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Functions, Zeta, Trace formulas | ||||||||
Journal or Publication Title: | Geometriae Dedicata | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0046-5755 | ||||||||
Official Date: | 1 August 2019 | ||||||||
Dates: |
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Volume: | 201 | ||||||||
Page Range: | pp. 155-186 | ||||||||
DOI: | 10.1007/s10711-018-0386-6 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 24 October 2018 | ||||||||
Date of first compliant Open Access: | 29 October 2018 |
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