2014/01/09 by Amy T. DeCelles, DeCelles, Amy T.
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1401.2015
10 pages, 1 figure. Augmented introduction, other minor changes to improve clarity. This is the version accepted by Michigan J. Math
arxiv created 2014/12/30 · arxiv updated 2014/12/31
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.