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On a Spectral Bound for Congruence Subgroup Families in SL(3,Z)

Timothy Christopher Heath

Title:
On a Spectral Bound for Congruence Subgroup Families in SL(3,Z)
Author(s):
Heath, Timothy Christopher
Thesis Advisor(s):
Goldfeld, Dorian
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Mathematics
Persistent URL:
Abstract:
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.
Subject(s):
Mathematics
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354
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Suggested Citation:
Timothy Christopher Heath, , On a Spectral Bound for Congruence Subgroup Families in SL(3,Z), Columbia University Academic Commons, .

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