Branching of Automorphic Fundamental Solutions
Number Theory
2014-12-31 v2
Abstract
Automorphic fundamental solutions and, more generally, solutions of automorphic differential equations, play a key role in the Diaconu-Garrett-Goldfeld prescription for spectral identities involving moments of L-functions as well as other applications, including an explicit formula relating the number of lattice points in a symmetric space to the automorphic spectrum. In this paper we discuss two cases in which the automorphic fundamental solution exhibits branching: pathwise meromorphic continuations may differ by a term involving an Eisenstein series.
Keywords
Cite
@article{arxiv.1401.2015,
title = {Branching of Automorphic Fundamental Solutions},
author = {Amy T. DeCelles},
journal= {arXiv preprint arXiv:1401.2015},
year = {2014}
}
Comments
10 pages, 1 figure. Augmented introduction, other minor changes to improve clarity. This is the version accepted by Michigan J. Math