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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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
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:	Date Event 1 August 2019 Published 7 September 2018 Available 18 August 2018 Accepted
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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