A Spectral reciprocity formula and non-vanishing for L-functions on GL(4)xGL(2)
Number Theory
2019-02-28 v2
Abstract
We develop a reciprocity formula for a spectral sum over central values of L-functions on GL(4)xGL(2). As an application we show that for any self-dual cusp form Pi for SL(4,Z), there exists a Maass form pi for SL(2,Z) such that L(1/2, Pi x pi) is nonvanishing. An important ingredient is a "balanced" Voronoi summation formula involving Kloosterman sums on both sides, which can also be thought of as the functional equation of a certain double Dirichlet series involving Kloosterman sums and GL(4) Hecke eigenvalues.
Keywords
Cite
@article{arxiv.1705.04344,
title = {A Spectral reciprocity formula and non-vanishing for L-functions on GL(4)xGL(2)},
author = {Valentin Blomer and Xiaoqing Li and Stephen D. Miller},
journal= {arXiv preprint arXiv:1705.04344},
year = {2019}
}
Comments
44 pages