The Voronoi formula on GL(3) with ramification

Abstract

Firstly we prove that the Voronoi formula of Miller-Schmid type applies to automorphic forms on GL(3) for the congruence subgroup ${\Gamma }_0(N)$, 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 ${\Gamma }_0(N)$, when the conductor of the additive character in the formula is coprime with $N$.

two new sections added