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The Voronoi formula on GL(3) with ramification
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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 $N$.
Forward citations
Cited by 3 Pith papers
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Pullbacks of Saito-Kurokawa lifts of square-free levels, their non-vanishing and the $L^2$-mass
For odd square-free levels, the pullback of a Saito-Kurokawa lift decomposes into old and new pieces whose squared norms are exactly the central L-values L(f⊗sym^2 g, 1/2), with all other pieces vanishing.
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First moments of ${\rm{GL}} (3) \times {\rm{GL}} (2)$ and ${\rm{GL}} (2)$ $L$-functions and their applications
The paper establishes a new simultaneous level-aspect subconvexity range for self-dual GL(3)xGL(2) L-functions and a Lindelof average bound in the weight aspect.
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Hybrid bounds for ${\rm{GL}}(4)\times {\rm{GL}}(1)$ twisted $L$-functions
A hybrid subconvex bound for L(1/2, Pi tensor chi) is claimed for prime level P and conductor M with M^{1/5} < P < M^{2/5}, but the final exponent passage in the proof is not justified.
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