Zeta Functions on Arithmetic Surfaces
Number Theory
2015-03-03 v3
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.
Cite
@article{arxiv.1311.6964,
title = {Zeta Functions on Arithmetic Surfaces},
author = {Thomas Oliver},
journal= {arXiv preprint arXiv:1311.6964},
year = {2015}
}
Comments
28 pages. Numerous corrections from previous versions, and greater emphasis on exposition