The Voronoi formula on GL(3) with ramification

arXiv1806.10786MaRDI QIDQ6303616

Fan Zhou

Publication date: 28 June 2018

Abstract: Firstly we prove that the Voronoi formula of Miller-Schmid type applies to automorphic forms on GL(3) for the congruence subgroup $Gamm{a}_0(N)$, when the conductor of the additive character in the formula is a multiple of $N$. As an application, we produce a result about the functional equation of $L$-function of the automorphic form on GL(3) twisted by Dirichlet characters. Secondly we prove that a similar formula applies to automorphic forms on GL(3) for the congruence subgroup $Gamm{a}_0(N)$, when the conductor of the additive character in the formula is coprime with $N$.

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) Fourier coefficients of automorphic forms (11F30)

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