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

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.

arXiv comment43 pages

References in corpus (2)

• The effect of convolving families of L-functions on the underlying group symmetries
• Low-lying Zeros of Cuspidal Maass Forms

Cited by in corpus (5)

• Low-lying zeroes of Maass form $L$-functions
• Plancherel distribution of Satake parameters of Maass cusp forms on $G{L}_3$
• Parametrization of Kloosterman sets and ${\mathrm{SL}}_3$-Kloosterman sums
• Recurrence relations for Mellin transforms of $GL(n,\mathbb{R})$ Whittaker functions
• Some Results in the Theory of Low-lying Zeros: Determining the 1-level density, identifying the group symmetry and the arithmetic of moments of Satake parameters