Fuchsian group


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Fuchsian group

[′fyük·sē·ən ‚grüp]
(mathematics)
A Kleinian group G for which there is a region D in the complex plane, consisting of either the interior of a circle or the portion of the plane on one side of a straight line, such that D is mapped onto itself by every element of G.
References in periodicals archive ?
Let [GAMMA] [subset] c PSL(2, R) be a strictly hyperbolic Fuchsian group acting on the upper half-plane H equipped with the hyperbolic metric.
The main theorem of [14, Theorem 5.3] states that a finitely generated, finite coarea Fuchsian group [GAMMA] admits a DF-domain if and only if [GAMMA] is an index 2 subgroup of a reflection group.
Let [GAMMA] [subset] PSL(2, R) be a cofinite Fuchsian group. Denote
Let r be the Fuchsian group of a Riemann surface of class [O.sub.G] acting on the unit disk D.
The Riemann zeta or Dirichlet L-functions (X = Z, Prim(Z) = {prime numbers}, N(p) = p, [rho] = Dirichlet character, n = 1) and the Selberg zeta function (X = [GAMMA]: a Fuchsian group, Prim([GAMMA]) = {prime geodesics in [GAMMA]\H} with H the upper half plane, N(p) = [e.sup.lentgh(p)], [rho] a unitary representation of [GAMMA], n = dim [rho]) satisfy this assumption.
On Relations between Fuchsian Groups, Fundamental Domains and Outer Billiards.
Series, "Markov maps associated with fuchsian groups," Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques, vol.
Young researchers were exposed to the basic theory of the two in lectures on interval exchange maps and translation surfaces; unipotent flows and applications; quantitative nondivergence and its Diophantine applications; diagonal actions on locally homogenous spaces; and Fuchsian groups, geodesic flows on surfaces of constant negative curvature, and symbolic coding of geodesics.
Pommerenke, On the Green's function of Fuchsian groups, Ann.
Papers cover such subjects as outer automorphism groups of certain orientable Seifert three-manifold groups, a proposed public key cryptosystem using the modular group, normal subgroups of themodular group and other Hecke groups, unions of varieties and quasi-varieties, context-free irreducible word problems in groups, informative words and discreteness, using group theory for knowledge representation and discovery, torsion in maximal arithmetic Fuchsian groups, density of test elements in finite Abelian groups and the Rosenberg "monster."
Eleven chapters cover linear transformations, groups of linear transformations, Fuchsian groups, the Poincare theta series, the elementary groups, the elliptic modular functions, conformal mapping, uniformization and elementary and Fuchsian functions, uniformization and groups of Schottky type, and differential equations.