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.
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We thank Peter Sarnak for helpful comments and the anonymous referees for their valuable feedback and corrections.
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Communicated by J. Marklof
The authors were partially supported by EPSRC Grant EP/K034383/1.
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Booker, A.R., Platt, D.J. Turing’s Method for the Selberg Zeta-Function. Commun. Math. Phys. 365, 295–328 (2019). https://doi.org/10.1007/s00220-018-3243-4
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DOI: https://doi.org/10.1007/s00220-018-3243-4