Analysis on arithmetic quotients: SL(2) Arithmetic subgroups of SL2(R)
نویسنده
چکیده
For (b), let Θ be any subset of Γ, x in its complement, U as in (a). The neighbourhood xU of x contains at most one element of Γ. There exists a neighbourhood of x contained in xU and not containing any element of Θ. For (c), let V be the closure of U ·U, which is compact. The intersection of Γ with V is compact, and covered by disjoint neighbourhoods of each of its points. This intersection must therefore be finite.
منابع مشابه
Discreteness Criterion for Subgroups of Products of Sl(2)
Let G be a finite product of SL(2,Ki)′s for local fields Ki of characteristic zero. We present a discreteness criterion for non-solvable subgroups of G containing an irreducible lattice of a maximal unipotent subgroup of G. In particular such a subgroup has to be arithmetic. This extends a previous result of A. Selberg when G is a product of SL2(R)′s.
متن کاملAnalysis on arithmetic quotients: SL(2) Classical and adelic automorphic forms
This essay will exhibit the realization of discrete series representations of SL 2 (R) on spaces of holomor-phic functions and relate them to automorphic forms for certain arithmetic groups. In a second essay I shall relate these in turn to representations of adèle groups, and more generally make remarks about the connection between arithmetic quotients and adelic quotients. By now the realizat...
متن کاملThe cusp amplitudes and quasi - level of a congruence subgroup of SL 2 over any Dedekind domain
This is the latest part of an ongoing project aimed at extending algebraic properties of the classical modular group SL2(Z) to equivalent groups in the theory of Drinfeld modules. We are especially interested in those properties which are important in the classical theory of modular forms. Our results are intended to be applicable to the theory of Drinfeld modular curves and forms. Here we are ...
متن کاملAlgebraic Curves Uniformized by Congruence Subgroups of Triangle Groups
We construct certain subgroups of hyperbolic triangle groups which we call “congruence” subgroups. These groups include the classical congruence subgroups of SL2(Z), Hecke triangle groups, and 19 families of arithmetic triangle groups associated to Shimura curves. We determine the field of moduli of the curves associated to these groups and thereby realize the groups PSL2(Fq) and PGL2(Fq) regul...
متن کاملGenera of Arithmetic Fuchsian Groups
Introduction. The fundamental invariant of a Riemann surface is its genus. In this paper, using arithmetical means, we calculate the genus of certain Riemann surfaces defined by unit groups in quaternion algebras. First we recall a well-known general construction of Riemann surfaces. The group SL2(R) acts on the upper half-plane H by Möbius transformations. If G is a Fuchsian group, that is, a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011