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Riemann surfaces (Q5904534)

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scientific article; zbMATH DE number 3695576

Language	Label	Description	Also known as
English	Riemann surfaces	scientific article; zbMATH DE number 3695576

Statements

scholarly article

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Riemann surfaces (English)

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O. V. Shvartsman

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Ernest B. Vinberg

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Journal of Soviet Mathematics

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publication date

1980

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zbMATH Keywords

Riemann surfaces

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Fuchsian groups

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Teichmüller spaces

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spaces of moduli

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Weil model

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Bers model

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Weierstraß points

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Torelli space

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Siegel halfspace

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automorphic forms

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MaRDI profile type

MaRDI publication profile

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Teichmüller problem for one class of open Riemannian surfaces

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Moduli of Riemann surfaces

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Automorphisms of Riemann surfaces

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Some classical theorems on open Riemann surfaces

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On the Number of Automorphisms of a Closed Riemann Surface

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Some remarks on Teichmüller's space of Riemann surfaces

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Curvature properties of Teichmüller's space

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Quasiconformal reflections

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Riemann's mapping theorem for variable metrics

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Analytic and harmonic obstruction on nonorientable Klein surfaces

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Analytic geometry on real algebraic curves

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On Cauchy's theorem for real algebraic curves with boundary

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Klein surfaces and real algebraic function fields

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Weierstrass points at cusps of \(\Gamma_ 0(n)\)

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Explicit Gap Series at Cusps of Γ(p)

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Hecke operators on \(\Gamma_0(m)\)

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On the moduli Jacobian varieties

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The Hausdorff Dimension of Singular Sets of Properly Discontinuous Groups

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The Exponent of Convergence of Poincaré Series

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Inequalities for certain Fuchsian groups

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On the Isometric Circles of Elements in a Fuchsian Group

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Prym varieties and Schottky problem

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Normal Subgroups of Fuchsian Groups with Fixed Parabolic Class Number

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Holomorphic differentials as functions of moduli

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Automorphic Forms and Poincare Series for Infinitely Generated Fuchsian Groups

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A non-standard integral equation with applications to quasi-conformal mappings

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Fiber spaces over Teichmüller spaces

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Holomorphic convexity of Teichmüller spaces

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Subgroups of One-Relator Fuchsian Groups

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The Symplectic Representation of Map Automorphisms

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Mapping class groups and their relationship to braid groups

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On braid groups

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Abelian quotients of the mapping class group of a 2-manifold

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Isotopies of homeomorphisms of Riemann surfaces and a theorem about Artin's braid group

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On isotopies of homeomorphisms of Riemann surfaces

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Examples of modular forms

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Generators of Fuchsian groups

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On Differentials of the First Kind and Theta Constants for Certain Congruence Subgroups

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Die Gruppe der Abbildungsklassen. (Das arithmetische Feld auf Flächen.)

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On the density of Strebel differentials

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Weierstraß-Punkte und kanonische stetige Familien von Riemannschen Metriken auf regulären Familien kompakter Riemannscher Flächen

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Die Automorphismengruppe der universellen Familie kompakter Riemannscher Flächen vom Geschlecht \(g\geq 3\)

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Weierstraß-Punkte und kanonische Familien von Riemannschen Metriken auf regulären Familien kompakter Riemannscher Flächen. II

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Einige Bemerkungen zum Weierstraßschen Lückensatz

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The Teichmüller space of an arbitrary Fuchsian group

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A Reproducing Formula for Integrable Automorphic Forms

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Reduced Teichmuller Spaces

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The contractibility of certain Teichmüller spaces

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On holomorphic cross-sections in Teichmüller spaces

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On holomorphic families of pointed Riemann surfaces

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A fibre bundle description of Teichmüller theory

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On isometries between Teichmüller spaces

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Some properties of Poincaré series of dimension \(-2\)

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Teichmuller Spaces and Representability of Functors

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A fundamental region for Hecke's modular group

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Modular Forms on Hecke's Modular Groups

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Special Divisors and Analytic Subloci of Teichmueller Space

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Automorphisms of compact Riemann surfaces and the vanishing of theta constants

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Special Divisors on Compact Riemann Surfaces

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THETA CONSTANTS, MODULI, AND COMPACT RIEMANN SURFACES

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Weierstrass Points and Analytic Submanifolds of Teichmueller Space

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Abelian Differentials with Double Zeros

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RELATIONS BETWEEN TWO KINDS OF THETA CONSTANTS ON A RIEMANN SURFACE

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TWO KINDS OF THETA CONSTANTS AND PERIOD RELATIONS ON A RIEMANN SURFACE

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Period relations of Schottky type on Riemann surfaces

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Theta functions on Riemann surfaces

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Tables of genera of groups of linear fractional transformations

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A note on finite groups which act freely on closed surfaces

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An Analysis of the Group Operation in Universal Teichmuller Space

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Maximal Fuchsian groups

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Fundamental polygons for Fuchsian groups

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Normal subgroups of the modular group

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Positive holomorphic differentials on Klein surfaces

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Introduction à la théorie des surfaces de Riemann

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Lectures on Riemann Surfaces: Jacobi Varieties

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Immersion of open Riemann surfaces

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Non-hyperelliptic Riemann surfaces

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CYCLIC GROUPS OF AUTOMORPHISMS OF A COMPACT RIEMANN SURFACE

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Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung

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On the number of 1-1 directly conformal maps which a multiply-connected plane region of finite connectivity 𝑝({>2}) admits onto itself

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On Schottky and Teichmüller spaces

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Local isometries of flat tori

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Bestimmung der Kommensurabilitätsklasse der Hilbertschen Modulgruppe

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On the Commensurability Class of the Rational Modular Group

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Diskrete Untergruppen von \(SL_2 (R)\).

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Note über das Geschlecht gewisser arithmetischer Gruppen

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Über den Raum der kompakten Riemannschen Flächen vom Geschlecht 2.

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Subgroups of finite index of Fuchsian groups

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Subgroups of infinite index in Fuchsian groups

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Subgroups of NEC groups

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A note on a paper of Farkas

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On analytic self-mappings of Riemann surfaces

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On Discrete Groups of Mobius Transformations

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Some extreme discrete groups

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On the number of automorphisms of a compact bordered Riemann surface

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Analytic self-mapping reducing to the identity mapping

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Analytic self-mapping inducing the identity on $H(W Z/(mZ))$

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Canonical polygons for finitely generated Fuchsian groups

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Intrinsic moduli on Riemann surfaces

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A Correction to "On Fricke Moduli"

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The modular group and Riemann surfaces of genus two

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Rings of Meromorphic Functions on Non-Compact Riemann Surfaces

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Automorphism Groups on Compact Riemann Surfaces

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Complex Structures on Riemann Surfaces

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Doubly generated Fuchsian groups

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A Note on Subgroups of the Modular Group

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Congruence subgroups of positive genus of the modular group

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On the Ring of Holomorphic Functions on an Open Riemann Surface

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On Teichmuller Spaces for Finitely Generated Fuchsian Groups

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On new kinds of Teichmüller spaces

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On Analytic Families of Compact Riemann Surfaces with Non-Trivial Automorphisms

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Holomorphic differentials on open Riemann surfaces

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On the Dimension of Varieties of Special Divisors

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On the dimension of varieties of special divisors. II

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Weierstrass points of the universal curve

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Degeneration of a compact Riemann surface of genus 2

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Handle removal on a compact Riemann surface of genus 2

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A remark on degeneration of a compact Riemann surface of genus 2

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Some degenerations of a compact Riemann surface of genus 4

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Automorphic integrals with preassigned periods

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On the boundedness of integrable automorphic forms

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Uniqueness of a class of Fuchsian groups

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Real Two-Dimensional Representations of the Modular Group and Related Groups

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On Riemann surfaces with maximal automorphism groups

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Über Spitzen diskontinuierlicher Gruppen von lineargebrochenen Transformationen

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Über die Heckeschen Gruppen \({\mathfrak G}(\lambda)\)

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Über die Heckeschen Gruppen \(G(\lambda)\). II

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Differentials and Metrics on Riemann Surfaces

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Newforms and functional equations

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A Comparison of Metrics on Teichmuller Space

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Riemann surface transformation groups

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Pairs of real 2-by-2 matrices that generate free products

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Groups Generated by two Parabolic Linear Fractional Transformations

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On a Theorem of Hurwitz

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On a Curve of Genus 7

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Geometrical realization of isomorphisms between plane groups

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The Classification of Non-Euclidean Plane Crystallographic Groups

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Action of Automorphisms of a Compact Riemann Surface on the First Homology Group

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Groups of hyperbolic crystallography

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Spaces of Subgroups and Teichmüller Space

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A Bound for the Number of Automorphisms of a Compact Riemann Surface

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Maximal normal Fuchsian groups

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Modulus Space is Simply-Connected

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SMOOTH COVERINGS OF HYPERELLIPTIC SURFACES

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Weierstrass Points on Compact Riemann Surfaces

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On Schoeneberg's theorem

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On Mapping-Class Groups and Teichmüller Spaces

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Braids and riemann surfaces

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Branched Structures on Riemann Surfaces

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On finitely generated Fuchsian groups

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On homotopic mappings of Riemann surfaces

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Moduli of marked Riemann surfaces

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Lattice subgroups of free congruence groups

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On a class of geodesics in Teichmüller space

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Notes on the Riemann-Roch theorem on open Riemann surfaces

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Automorphisms of compact Klein surfaces with boundary

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Classification of Normal Congruence Subgroups of the Modular Group

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On the genus of fields of elliptic modular functions

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Eine Bemerkung über Fuchssche Gruppen

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On the Growth of the Taylor Coefficients of Automorphic Forms

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On Integrable and Bounded Automorphic Forms

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On Integrable and Bounded Automorphic Forms. II

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Fuchsian Groups of Convergence Type and Nontangential Growth of Automorphic Forms

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On Cycloidal Subgroups of the Modular Group<sup>†</sup>

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Subgroups of the Classical Modular Group

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Fixed Points of Automorphisms of Compact Riemann Surfaces

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Riemann Surfaces as Orbit Spaces of Fuchsian Groups

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Abelian quotients of the Teichmüller modular group

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Ein Approximationssatz für die Fuchsschen Gruppen

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Divisors on meromorphic function fields

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A Note on Modular Groups

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Normal Congruence Subgroups of the Modular Group

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A Complete Description of the Normal Subgroups of Genus One of the Modular Group

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Normal Subgroups of the Modular Group which are not Congruence Subgroups

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Classification of Normal Subgroups of the Modular Group

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Maximal Normal Subgroups of the Modular Group

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Pairs of matrices generating discrete free groups and free products

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Conjugacy, genus, and class numbers

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Transitive horocyles for Fuchsian groups

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Transitivity Properties of Fuchsian Groups

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Characterization of Fuchsian groups whose integrable forms are bounded

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Abbildungsklassen endlicher Ordnung

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Notes on conformal mappings of a Riemann surface onto itself

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The Teichmuller Spaces are Distinct

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Some Remarks on the Moduli of Punctured Spheres

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The limit set of a Fuchsian group

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Diophantine approximation in Fuchsian groups

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Über eine Metrisierung der automorphen Formen und die Theorie der Poincaréschen Reihen

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Über einen einfachen Typus von Untergruppen der Modulgruppe

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Über die Kongruenzgruppen der Stufe 4.

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Über ein Spurbildung bei automorphen Formen

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Über die Konstruktion zykloider Kongruenzgruppen in der rationalen Modulgruppe.

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Über die Primformen der Hauptkongruenzgruppen

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Konstruktionsprinzipien für Untergruppen der Modulgruppen mit einer oder zwei Spitzenklassen.

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On a conjecture of H. Rauch on theta constants and Riemann surfaces with many automorphisms.

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Real two-dimensional representations of two generator free groups

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Two generator discrete free products

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Canonical generators of Fuchsian groups

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All two generator Fuchsian groups

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Two generator Fuchsian groups of genus one

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Correction to ''Two generator Fuchsian groups of genus one''

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Diophantine Approximation and Horocyclic Groups

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Hecke operators on congruence subgroups of the modular group

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Lattice subgroups of free congruence groups

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Subgroups of the modular group generated by parabolic elements of constant amplitude

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On the Boundedness of p-Integrable Automorphic Forms

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Weierstrass points, branch points, and moduli of riemann surfaces

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A transcendental view of the space of algebraic Riemann surfaces

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The local ring of the genus three modulus space at Klein’s 168 surface

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Theta constants of two kinds on a compact Riemann surface of genus 2

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Subgroups of the Unimodular Group

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Sur les polygones générateurs de groupes fuchsiens

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Almost isometries of Banach spaces and moduli of Riemann surfaces

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Almost isometries of Banach spaces and moduli of Riemann surfaces. II

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Continuation of Riemann Surfaces

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Finitely generated Fuchsian groups and character-automorphic normal functions

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An arithmetic characterization of the parabolic points of <i>G</i>(2cos π/5)

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Fuchssche Gruppen, die freies Produkt zweier zyklischer Gruppen sind, und die Gleichung \(x^2+y^2+z^2=xyz\).

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Report on the Teichmüller Metric

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Embeddings of open Riemann surfaces

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Groups related to compact Riemann surfaces

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Riemann matrices for hyperelliptic surfaces with involutions other than the interchange of sheets

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Moduli for Special Riemann Surfaces of Genus 2

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On the Riemann-Roch theorem on open Riemann surfaces

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Hyperbolic Generators for Fuchsian Groups

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Symmetric Fuchsian Groups

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Some remarks on discontinuous groups

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Subgroups of Fuchsian Groups and Finite Permutation Groups

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Automorphisms of compact non-orientable Riemann surfaces

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Finitely Maximal Fuchsian Groups

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Symmetries of Riemann surfaces with large automorphism group

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Automorphisms of Maps, Permutation Groups and Riemann Surfaces

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On Weierstrass points in the theory of elliptic modular forms

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On Teichmüller spaces of tori

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Impossible specifications for the modular group

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Fuchsian groups contained in \(SL_ 2(\mathbb{Q})\)

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Planar Coverings of Closed Riemann Surfaces

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On quadratic differentials with closed trajectories and their applications

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Einbettungen endlicher Riemannscher Flächen

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On conformal mapping of a hyperelliptic Riemann surface onto itself

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Conformal automorphisms of a compact bordered Riemann surface of genus $3$

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On non-Euclidean crystallographic groups

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An extension of F. Klein's level concept

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On some representations of \(SL(2,\mathbb{Z})\)

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Noncompleteness of the Weil-Petersson metric for Teichmüller space

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A Uniformization Theorem for Arbitrary Riemann Surfaces with Signature

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A Continuity Theorem for Fuchsian Groups

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Anticonformal Automorphisms of Compact Riemann Surfaces

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Über Automorphismen ebener diskontinuierlicher Gruppen

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Über die Nielsensche Kürzungsmethode in freien Produkten mit Amalgam

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On the homeotopy groups of surfaces

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Addendum to: “On extensions of fundamental groups of surfaces and related groups”

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Über Erzeugende ebener diskontinuierlicher Gruppen

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Finite extensions of non-Euclidean crystallographic groups

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Eine Verallgemeinerung der Formel von Riemann-Hurwitz. (A generalization of the Riemann-Hurwitz formula)

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full work available at URL

https://doi.org/10.1007/bf01097782

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Identifiers

zbMATH Open document ID

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10.1007/BF01097782

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5904534

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