On Selberg's small eigenvalue conjecture and residual eigenvalues

DOI10.1515/CRELLE.2011.050zbMath1237.11024arXiv0707.2332WikidataQ122928627 ScholiaQ122928627MaRDI QIDQ5198594

Morten S. Risager

Publication date: 8 August 2011

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.2332

zbMATH Keywords

Selberg trace formulaspecial values of \(L\)-functionsSelberg's conjectureKato perturbation theory

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

Noncongruence subgroups and Maass waveforms

Cites Work

• On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\)
• Modular forms of varying weight. II
• Geodesics in homology classes
• Asymptotics for closed geodesics in a homology class, the finite volume case
• Nonvanishing of \(L\)-functions for \(\mathrm{GL}(2)\)
• The spectrum of Fermat curves
• A remark on the discrete spectrum of the automorphic Laplacian for a generalized cycloidal subgroup of a general Fuchsian group
• Cusp forms for character varieties
• Disappearance of cusp forms in special families
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• On the asymptotic behavior of counting functions associated to degenerating hyperbolic Riemann surfaces
• Newforms and functional equations
• The subconvexity problem for Artin \(L\)-functions
• Modular symbols have a normal distribution
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• On Selberg's eigenvalue conjecture
• Hecke operators on \(\Gamma_0(m)\)
• Equidistribution of geodesics on homology classes and analogues for free groups
• Fourier coefficients of Eisenstein series on non-congruence subgroups
• Small eigenvalues of the Laplace operator on compact Riemann surfaces
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Nonvanishing of \(L\)-values and the Weyl law
• Spectral theory of Laplacians for Hecke groups with primitive character
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