Date of Award

1-1-2010

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (v, 50 pages)

Dissertation/Thesis Chair

George E Andrews

Committee Members

George E Andrews, Antun Milas, Heekyoung Hahn, Anupam Srivastav

Keywords

Integer Partitions, Number Theory, Ramanujan, Partitions (Mathematics), Polynomials, Numerical analysis

Subject Categories

Physical Sciences and Mathematics

Abstract

Though congruence properties of p(n) modulo an odd prime L have been well studied since the time of Ramanujan, congruence properties of p(n,m) modulo L were unknown beyond L=3. The purpose of this thesis is to detail the discovery and proofs of several infinite families of congruence properties of p(n,m) modulo every odd prime L. We will also prove a striking congruence relationship of the form p(n,m) congruent to p(n',m) modulo L.

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