Date of Award

5-2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Number Theory

Advisor

James, Kevin

Committee Member

Brown , Jim

Committee Member

Calkin , Neil

Abstract

This thesis is a presentation of some of my research activities while at Clemson University. In particular this includes joint work on the factorization of eigenforms and their relationship to Rankin- Selberg L-values, and nearly holomorphic eigenforms. The main tools used on the factorization of eigenforms are linear algebra, the j function, and the Rankin-Selberg Method. The main tool used on nearly holomorphic modular forms is the Rankin-Cohen bracket operator.

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