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Summation Formulas, from Poisson and Voronoi to the Present

Stephen D. Miller·Wilfried Schmid
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Abstract

We give an overview of classical summation formulations, such as Poisson's and Voronoi's, and then turn to modern versions involving modular form coefficients. A new formula involving the coefficients of cusp forms on GL(3) is described, and its proof sketched, followed by applications to L-functions. The main method used is the boundary value distribution of automorphic forms.

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Stephen D. Miller, Wilfried Schmid. 2003-04-15. Summation Formulas, from Poisson and Voronoi to the Present. https://arxiv.org/abs/math/0304187

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