The Voronoi formula and double Dirichlet series

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.

minor revision

References in corpus (1)

• Voronoi Summation Formulae on GL(n)

Cited by in corpus (2)

• The balanced Voronoi formulas for GL(n)
• Dirichlet twists of ${\mathrm{GL}}_n$-automorphic $L$-functions and hyper-Kloosterman Dirichlet series