Strong spectral gaps for compact quotients of products of \(\text{PSL}(2,\mathbb R)\)

DOI10.4171/JEMS/151zbMath1254.11050arXiv0808.2368OpenAlexW2137053050MaRDI QIDQ1012481

Dubi Kelmer, Peter C. Sarnak

Publication date: 21 April 2009

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.2368

zbMATH Keywords

Selberg trace formulaspectral gapproduct of hyperbolic planes

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

Polynomial mixing for time-changes of unipotent flows ⋮ Exponential multiple mixing for some partially hyperbolic flows on products of \(\mathrm{PSL}(2, \mathbb{R})\) ⋮ Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow ⋮ Quantitative multiple mixing ⋮ Prime and almost prime integral points on principal homogeneous spaces ⋮ Time change for unipotent flows and rigidity ⋮ Hybrid trace formula for a non-uniform irreducible lattice in \(\mathrm{PSL}_2(\mathbb R)^n\) ⋮ Ergodic theory and the duality principle on homogeneous spaces ⋮ Cocycle rigidity and splitting for some discrete parabolic actions ⋮ Counting orbits of integral points in families of affine homogeneous varieties and diagonal flows ⋮ The hyperbolic lattice point count in infinite volume with applications to sieves ⋮ Central limit theorem and cohomological equation on homogeneous spaces ⋮ Extreme value distributions for one-parameter actions on homogeneous spaces

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