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.
CITATION STYLE
Miller, S. D., & Schmid, W. (2004). Summation formulas, from Poisson and Voronoi to the present. In Noncommutative Harmonic Analysis (pp. 419–440). Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8204-0_15
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