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

zbMath1344.11041arXiv1203.6667MaRDI QIDQ5494368

Dorian Goldfeld, Alex V. Kontorovich

Publication date: 27 July 2014

Full work available at URL: https://arxiv.org/abs/1203.6667

zbMATH Keywords

Fourier transformcontinuous spectrum\(L\)-functionWhittaker functionKuznetsov formulasymmetry type

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (13)

Parametrization of Kloosterman sets and \(\mathrm{SL}_3\)-Kloosterman sums ⋮ Some Results in the Theory of Low-Lying Zeros of Families of L-Functions ⋮ Families of L-Functions and Their Symmetry ⋮ Determining optimal test functions for 2-level densities ⋮ Applications of the Kuznetsov formula on \(\mathrm{GL}(3)\) ⋮ Recurrence relations for Mellin transforms of \(G L(n, \mathbb{R})\) Whittaker functions ⋮ Weighted Sato-Tate vertical distribution of the Satake parameter of Maass forms on \(\mathrm{PGL}(N)\) ⋮ One-level density for holomorphic cusp forms of arbitrary level ⋮ The Spectral Kuznetsov Formula on $SL(3)$ ⋮ The Relative Trace Formula in Analytic Number Theory ⋮ Applications of analytic newvectors for \(\operatorname{GL}(N)\) ⋮ An orthogonality relation for (with an appendix by Bingrong Huang) ⋮ Low-lying zeros of \(L\)-functions for quaternion algebras

This page was built for publication: On the GL(3) Kuznetsov Formula with applications to Symmetry Types of families of $L$-functions