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arXiv · 1203.6667

On the GL(3) Kuznetsov Formula with applications to Symmetry Types of families of $L$-functions

Dorian Goldfeld·Alex Kontorovich
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Abstract

We present an explicit approach to the GL(3) Kuznetsov formula. As an application, for a restricted class of test functions, we obtain the low-lying zero densities for the following three families: cuspidal GL(3) Maass forms phi, the symmetric square family sym^2 phi on GL(6), and the adjoint family Ad phi on GL(8). Hence we can identify their symmetry types; they are: unitary, unitary, and symplectic, respectively.

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Dorian Goldfeld, Alex Kontorovich. 2012-03-29. On the GL(3) Kuznetsov Formula with applications to Symmetry Types of families of $L$-functions. https://arxiv.org/abs/1203.6667

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