Arithmetic groups and the length spectrum of Riemann surfaces

DOI10.1215/S0012-7094-96-08407-0zbMath0867.30030OpenAlexW1484848569MaRDI QIDQ1922424

Paul Schmutz Schaller

Publication date: 4 August 1997

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-96-08407-0

Mathematics Subject Classification ID

Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (10)

Partial solution of a conjecture of Schmutz ⋮ Examples of infinite covolume subgroups of PSL\((2, \mathbb R)^r\) with big limit sets ⋮ Stable multiplicities in the length spectrum of Riemann surfaces ⋮ Equivalent trace sets for arithmetic Fuchsian groups ⋮ Closed geodesics on pairs of pants ⋮ The joint spectrum ⋮ Geometry of Riemann surfaces based on closed geodesics ⋮ The modular torus has maximal length spectrum ⋮ On arithmetic Fuchsian groups and their characterizations. ⋮ Traces, lengths, axes and commensurability

Cites Work

• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen
• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II
• Arithmetic subgroups of algebraic groups
• Arithmétique des algèbres de quaternions
• A characterization of arithmetic Fuchsian groups
• Arithmetic triangle groups
• Number variance for arithmetic hyperbolic surfaces
• Riemann surfaces with shortest geodesic of maximal length
• Congruence subgroups and maximal Riemann surfaces
• Spectral geometry and scattering theory for certain complete surfaces of finite volume
• Geometry and spectra of compact Riemann surfaces
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