We prove a Voronoi formula for coefficients of a large class of -functions including Maass cusp forms, Rankin–Selberg convolutions, and certain noncuspidal forms. Our proof is based on the functional equations of -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.
"The Voronoi formula and double Dirichlet series." Algebra Number Theory 10 (10) 2267 - 2286, 2016. https://doi.org/10.2140/ant.2016.10.2267