Branching of Automorphic Fundamental Solutions

Amy T. DeCelles

Branching of Automorphic Fundamental Solutions

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arxiv 1401.2015 v2 pith:JKSJRARG submitted 2014-01-09 math.NT

Branching of Automorphic Fundamental Solutions

Amy T. DeCelles This is my paper

classification math.NT

keywords automorphicfundamentalsolutionsbranchinginvolvingapplicationscasescontinuations

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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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