Congruence subgroups and maximal Riemann surfaces

DOI10.1007/BF02921547zbMath0804.32010MaRDI QIDQ1329634

Paul Schmutz Schaller

Publication date: 12 July 1994

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

Riemann surfaceseigenvaluesTeichmüller spaceLaplacianSelberg conjectureshortest closed geodesic

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Geodesics in global differential geometry (53C22) Teichmüller theory for Riemann surfaces (30F60)

Related Items

Local maxima of the systole function, Construction of hyperbolic Riemann surfaces with large systoles, Arithmetic Fuchsian groups and the number of systoles, Systoles on Riemann surfaces, Compact Riemann surfaces with many systoles, Arithmetic groups and the length spectrum of Riemann surfaces, Growth of the Weil-Petersson inradius of moduli space, Hyperbolic punctured spheres without arithmetic systole maximizers, The homology systole of hyperbolic Riemann surfaces, Systoles and Dehn surgery for hyperbolic 3-manifolds, Systole growth for finite area hyperbolic surfaces, Simple geodesics and Markoff quads, The maximal injectivity radius of hyperbolic surfaces with geodesic boundary, On the hyperbolic distance of \(n\)-times punctured spheres, Infinite sequences of perfect Riemann surfaces, Lipschitz constants to curve complexes for punctured surfaces, Systolic cutting and inequalities for bordered hyperbolic surfaces, Systole and inradius of noncompact hyperbolic manifolds, Systoles of a Family of Triangle Surfaces, Extremal symplectic lattices, Geometry of Riemann surfaces based on closed geodesics, Hyperbolic surfaces with long systoles that form a pants decomposition

Cites Work

• Small eigenvalues of automorphic Laplacians in spaces of parabolic forms
• Kloosterman sums for Clifford algebras and a lower bound for the positive eigenvalues of the Laplacian for congruence subgroups acting on hyperbolic spaces
• Riemann surfaces with shortest geodesic of maximal length
• Arithmetic Fuchsian groups and the number of systoles
• Injectivity radius and low eigenvalues of hyperbolic manifolds.
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Kreisausfüllungen der hyperbolischen Ebene
• Geometry and spectra of compact Riemann surfaces
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