Summation Formulas, from Poisson and Voronoi to the Present

Mathematics – Number Theory

Scientific paper

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22 pages, to appear in "Non-commutative harmonic analysis: In honor of Jacques Carmona."

Scientific paper

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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