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Turing’s Method for the Selberg Zeta-Function

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Original languageEnglish
Pages (from-to)295-328
Number of pages34
JournalCommunications in Mathematical Physics
Issue number1
Early online date6 Sep 2018
DateSubmitted - 2 Oct 2017
DateAccepted/In press - 20 Jul 2018
DateE-pub ahead of print - 6 Sep 2018
DatePublished (current) - 24 Jan 2019


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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