منابع مشابه
Counting Congruence Subgroups
Abstract. Let Γ denote the modular group SL(2, Z) and Cn(Γ) the number of congruence subgroups of Γ of index at most n. We prove that lim n→∞ log Cn(Γ) (log n)2/ log log n = 3−2 √ 2 4 . We also present a very general conjecture giving an asymptotic estimate for Cn(Γ) for general arithmetic groups. The lower bound of the conjecture is proved modulo the generalized Riemann hypothesis for Artin-He...
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Let F be a finitely generated group. Denote by an(T) (resp.<rn(r)) the number of subgroups of F of index n (resp. of index at most n). This paper deals with the connection between the algebraic structure of the group F and the arithmetic properties of the sequence an(F), n — 1,2,3,..., e.g., the growth of the sequence an(T) ("the subgroup growth") or the properties of the function Cr(s) = X2£Li...
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Let K be a number field with r real places and s complex places, and let OK be the ring of integers of K. The quotient [H]×[H]/PSL2(OK) has hK cusps, where hK is the class number of K. We show that under the assumption of the generalized Riemann hypothesis that if K is not Q or an imaginary quadratic field and if i ∈ K, then PSL2(OK) has infinitely many maximal subgroups with hK cusps. A key el...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0314972-0