Summation Formulas, from Poisson and Voronoi to the Present
Number Theory
2007-05-23 v1 Representation Theory
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.
Cite
@article{arxiv.math/0304187,
title = {Summation Formulas, from Poisson and Voronoi to the Present},
author = {Stephen D. Miller and Wilfried Schmid},
journal= {arXiv preprint arXiv:math/0304187},
year = {2007}
}
Comments
22 pages, to appear in "Non-commutative harmonic analysis: In honor of Jacques Carmona."