Algebra & Number Theory

The Voronoi formula and double Dirichlet series

Eren Kıral and Fan Zhou

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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

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

Received: 8 May 2016
Revised: 19 July 2016
Accepted: 23 September 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F30: Fourier coefficients of automorphic forms
Secondary: 11F68: Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series 11L05: Gauss and Kloosterman sums; generalizations

Voronoi formula automorphic form Maass form multiple Dirichlet series Gauss sum Kloosterman sum Rankin–Selberg $L$-function


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.

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