Asymptotic trace formula for the Hecke operators

DOI10.1007/s00208-020-02054-wzbMath1465.11100arXiv1808.04015OpenAlexW3048081427WikidataQ126050052 ScholiaQ126050052MaRDI QIDQ2200774

Junehyuk Jung, Naser Talebizadeh Sardari

Publication date: 22 September 2020

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.04015

zbMATH Keywords

Hecke operatorsarithmetic quantum chaosPetersson trace formula

Mathematics Subject Classification ID

Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Hecke-Petersson operators, differential operators (one variable) (11F25)

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The remainder in Weyl's law for random two-dimensional flat tori
• Effective equidistribution of eigenvalues of Hecke operators
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• On the wave equation on a compact Riemannian manifold without conjugate points
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• Spectra of elements in the group ring of SU(2)
• Indivisibility of class numbers of imaginary quadratic fields and orders of Tate-Shafarevich groups of elliptic curves with complex multiplication
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• A formula for the traces of the Hecke operators on certain spaces of newforms
• Über die Entwicklungskoeffizienten der automorphen Formen
• La conjecture de Weil. I
• Optimal strong approximation for quadratic forms
• The spectral function of an elliptic operator
• Hecke operators on \(\Gamma_0(m)\)
• A central limit theorem for the spectrum of the modular domain
• Families of L-Functions and Their Symmetry
• The distribution of the eigenvalues of Hecke operators
• A new form of the circle method, and its application to quadratic forms.
• On the Holomorphy of Certain Dirichlet Series
• Semiclassical theory of spectral rigidity
• Mass equidistribution for Hecke eigenforms
• On the Bessel function in the transition region
• A relative trace formula proof of the Petersson trace formula
• Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
• Low lying zeros of families of \(L\)-functions

This page was built for publication: Asymptotic trace formula for the Hecke operators