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arXiv · 1705.04344

A Spectral reciprocity formula and non-vanishing for L-functions on GL(4)xGL(2)

Valentin Blomer·Xiaoqing Li·Stephen D. Miller
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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.

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Valentin Blomer, Xiaoqing Li, Stephen D. Miller. 2017-05-11. A Spectral reciprocity formula and non-vanishing for L-functions on GL(4)xGL(2). https://arxiv.org/abs/1705.04344

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