2015 Theses Doctoral

# 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.

## Subjects

## Files

- Heath_columbia_0054D_12515.pdf binary/octet-stream 445 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Goldfeld, Dorian
- Degree
- Ph.D., Columbia University
- Published Here
- February 24, 2015