Length spectra of the Hecke triangle groups

DOI10.1007/BF02572621zbMath0840.11019MaRDI QIDQ1909554

Thomas A. Schmidt, Mark Sheingorn

Publication date: 1 July 1996

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

Full work available at URL: https://eudml.org/doc/174816

zbMATH Keywords

fixed pointsquadratic formsHecke triangle groupexplicit construction of the geodesic length spectrumperiodicity of continued fraction expansion of quadratic irrationalities

Mathematics Subject Classification ID

Quadratic forms over global rings and fields (11E12) Structure of modular groups and generalizations; arithmetic groups (11F06) Continued fractions (11A55)

Related Items (20)

Conjugacy classes and rational period functions for the Hecke groups ⋮ Attractors of dual continued fractions ⋮ Distribution of approximants and geodesic flows ⋮ Transcendence with Rosen continued fractions ⋮ Relationships between fixed points and eigenvectors in the group \(\mathrm{GL}(2,\mathbb R)\). ⋮ Unnamed Item ⋮ Commensurable continued fractions ⋮ Power subgroups of some Hecke groups. ⋮ On numbers of the form \(n=x^2+Ny^2\) and the Hecke groups \(\mathcal H(\sqrt N)\) ⋮ A Hecke correspondence theorem for automorphic integrals with symmetric rational period functions on the Hecke groups ⋮ Normal Congruence Subgroups of Hecke Groups ⋮ Rosen fractions and Veech groups, an overly brief introduction ⋮ Principal congruence subgroups of Hecke groups \(H(\sqrt{q})\) ⋮ Unnamed Item ⋮ Hecke-symmetry and rational period functions ⋮ The finiteness of derivation-invariant prime ideals and the algebraic independence of the Eisenstein series ⋮ Congruence subgroups of Hecke groups ⋮ ON BINARY QUADRATIC FORMS AND THE HECKE GROUPS ⋮ Symbolic dynamics for the modular surface and beyond ⋮ Central points of the double heptagon translation surface are not connection points

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Der Überlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen
• Values of hypergeometric functions
• Diophantine approximation on hyperbolic orbifolds
• A reciprocity law for prime geodesics
• Eine arithmetische Eigenschaft automorpher Formen zu gewissen nicht- arithmetischen Gruppen
• Chaos in classical and quantum mechanics
• Über die Heckeschen Gruppen \(G(\lambda)\). II
• On the metrical transitivity of the geodesics on closed surfaces of constant negative curvature
• Über die Heckeschen Gruppen \({\mathfrak G}(\lambda)\)
• On the sum and product of continued fractions
• A class of continued fractions associated with certain properly discontinuous groups
• Distribution of closed geodesics on the modular surface and quadratic irrationals
• On the Cuspidal Spectrum of the Arithmetic Hecke Groups
• Modular embeddings for some non-arithmetic Fuchsian groups
• Simple closed geodesics on 𝐻⁺/Γ(3) arise from the Markov spectrum
• Diskrete Deformation Fuchsscher Gruppen und ihrer automorphen Formen.
• Diophantine approximation on Hecke groups
• The Markoff Spectrum in the Hecke Group G ₅
• Cusp forms and Hecke groups.
• Parabolic Cohomology of Arithmetic Subgroups of SL(2, Z ) with Coefficients in the Field of Rational Functions on the Riemann Sphere
• On the Fourier coefficients of triangle functions
• The Length Spectrum of a Riemann Surface is Always of Unbounded Multiplicity
• Graduierte Algebren automorpher Formen zu Dreiecksgruppen
• An Arithmetic-Geometric Method in the Study of the Subgroups of the Modular Group
• Hecke groups and continued fractions
• Transzendente Zahlen als Fourierkoeffizienten von Heckes Modulformen
• Trace Classes and Quadratic Forms in the Modular Group
• The Local Hurwitz Constant and Diophantine Approximation on Hecke Groups
• The nodal set of a finite sum of Maass cusp forms is a graph
• Class numbers of indefinite binary quadratic forms
• Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung

This page was built for publication: Length spectra of the Hecke triangle groups