Turing’s Method for the Selberg Zeta-Function

Andrew Booker; David J Platt

doi:10.1007/s00220-018-3243-4

Turing’s Method for the Selberg Zeta-Function

Andrew Booker^*, David J Platt

^*Corresponding author for this work

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Abstract

In one of his final research papers, Alan Turing introduced a method to certify the completeness of a purported list of zeros of the Riemann zeta-function. In this paper we consider Turing's method in the analogous setting of Selberg zeta-functions, and we demonstrate that it can be carried out rigorously in the prototypical case of the modular surface.

Original language	English
Pages (from-to)	295-328
Number of pages	34
Journal	Communications in Mathematical Physics
Volume	365
Issue number	1
Early online date	6 Sept 2018
DOIs	https://doi.org/10.1007/s00220-018-3243-4
Publication status	Published - 24 Jan 2019

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AB - In one of his final research papers, Alan Turing introduced a method to certify the completeness of a purported list of zeros of the Riemann zeta-function. In this paper we consider Turing's method in the analogous setting of Selberg zeta-functions, and we demonstrate that it can be carried out rigorously in the prototypical case of the modular surface.

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Turing’s Method for the Selberg Zeta-Function

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