## Algebra & Number Theory

### 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 noncuspidal forms. 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.

#### Article information

Source
Algebra Number Theory, Volume 10, Number 10 (2016), 2267-2286.

Dates
Revised: 19 July 2016
Accepted: 23 September 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.ant/1510842637

Digital Object Identifier
doi:10.2140/ant.2016.10.2267

Mathematical Reviews number (MathSciNet)
MR3582019

Zentralblatt MATH identifier
06664750

#### Citation

Kıral, Eren; Zhou, Fan. The Voronoi formula and double Dirichlet series. Algebra Number Theory 10 (2016), no. 10, 2267--2286. doi:10.2140/ant.2016.10.2267. https://projecteuclid.org/euclid.ant/1510842637

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