On a Spectral Bound for Congruence Subgroup Families in SL(3,Z)
Spectral bounds on Maass forms of congruence families in algebraic groups are important ingredients to proving almost prime results for these groups. Extending the work of Gamburd [Gamburd, 2002] and Magee [Magee, 2013], we produce a condition under which such a bound exists in congruence subgroup families of SL(3,Z), uniformly and even when these groups are thin, i.e. of infinite index. The condition is analogous to the cusp and collar lemmas in Gamburd's work and is expected to hold for families whose Hausdorff dimension of the limit set is large enough.
Academic Commons
Heath, Timothy Christopher
Author
Goldfeld, Dorian
Thesis advisor
Columbia University. Mathematics
Originator
Theses
English
Mathematics
text
2015
eng
2017-06-12T17:37:29Z
2017-06-12T18:36:46Z
Ph.D.
2
Mathematics
Columbia University
10.7916/D8XW4HNM