Branching of Automorphic Fundamental Solutions

Amy T. DeCelles

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arXiv · 1401.2015

Branching of Automorphic Fundamental Solutions

Amy T. DeCelles

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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.

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Amy T. DeCelles. 2014-01-09. Branching of Automorphic Fundamental Solutions. https://arxiv.org/abs/1401.2015

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