منابع مشابه
Counting Maximal Arithmetic Subgroups
for absolute constants C6, C7. This theorem (almost) follows from [EV, Theorem 1.1], the only point being to control the dependence of implicit constants on the degree of the number field. We refer to [EV] for further information and for some motivational comments about the method. In the proof C1, C2, . . . will denote certain absolute constants. A.2. Let K be an extension of Q of degree d ≥ 2...
متن کاملCounting Maximal Arithmetic Subgroups Mikhail Belolipetsky with an Appendix by Jordan Ellenberg and Akshay Venkatesh
We study the growth rate of the number of maximal arithmetic subgroups of bounded covolumes in a semi-simple Lie group using an extension of the method due to Borel and Prasad.
متن کاملCounting Maximal Arithmetic Subgroups Mikhail Belolipetsky with an Appendix by Jordan Ellenberg and Akshay Venkatesh
We study the growth rate of the number of maximal arithmetic subgroups of bounded covolumes in a semi-simple Lie group using an extension of the method due to Borel and Prasad. As an application we prove a nonuniform case of a conjecture of Lubotzky et al. on the growth of lattices in higher rank semi-simple Lie group H, which claims that the growth rate is asymptotically equal to the congruenc...
متن کاملCounting Maximal Arithmetic Subgroups Mikhail Belolipetsky with an Appendix by Jordan Ellenberg and Akshay Venkatesh
We study the growth rate of the number of maximal arithmetic subgroups of bounded covolumes in a semi-simple Lie group using an extension of the method due to Borel and Prasad.
متن کاملCounting 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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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2007
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-07-14011-0