Turing's method for the Selberg zeta-function

Published 2 Oct 2017 in math.NT | (1710.00603v3)

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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