Zeta Functions on Arithmetic Surfaces

Published 27 Nov 2013 in math.NT | (1311.6964v3)

Abstract: We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called mean-periodicity correspondence, which is comparable to the better known automorphicity conjectures for the generic fibre.

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Thomas Oliver

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