Density theorems for exceptional eigenvalues for congruence subgroups

DOI10.2140/ant.2018.12.1581zbMath1444.11105arXiv1609.06740OpenAlexW3104753384MaRDI QIDQ1621972

Peter J. Humphries

Publication date: 12 November 2018

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.06740

zbMATH Keywords

Ramanujan conjectureSelberg eigenvalue conjecture

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (9)

A random cover of a compact hyperbolic surface has relative spectral gap \(\frac{3}{16}-\varepsilon\) ⋮ An explicit formula for the second moment of Maass form symmetric square \(L\)-functions ⋮ Kloosterman sums do not correlate with periodic functions ⋮ The density hypothesis for horizontal families of lattices ⋮ ON A TWISTED VERSION OF LINNIK AND SELBERG'S CONJECTURE ON SUMS OF KLOOSTERMAN SUMS ⋮ Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field ⋮ Twist‐minimal trace formulas and the Selberg eigenvalue conjecture ⋮ Cutoff on hyperbolic surfaces ⋮ Motohashi’s formula for the fourth moment of individual DirichletL-functions and applications

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