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arXiv · 1508.01985

The Voronoi formula and double Dirichlet series

Eren Mehmet Kiral·Fan Zhou
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Abstract

We prove a Voronoi formula for coefficients of a large class of $L$-functions including Maass cusp forms, Rankin-Selberg convolutions, and certain isobaric sums. Our proof is based on the functional equations of $L$-functions twisted by Dirichlet characters and does not directly depend on automorphy. Hence it has wider application than previous proofs. The key ingredient is the construction of a double Dirichlet series.

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Eren Mehmet Kiral, Fan Zhou. 2016-05-09. The Voronoi formula and double Dirichlet series. https://doi.org/10.2140/ant.2016.10.2267

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