Doctoral Dissertations

Date of Award

5-2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Marie Jameson

Committee Members

Luis Finotti, Shashikant Mulay, Michael Berry

Abstract

This dissertation explores results pertaining to partition theory and its q-series identities using techniques from modular forms. In particular, Chapter 2 proves congruences for k-colored generalized Frobenius partitions originally dened by George Andrews in 1984. These congruences generalize parity results for the partition function and generalized Frobenius partitions to weakly holomorphic modular forms of a certain type. Chapter 3 gives results regarding the Andrews-Bressoud identities, a generalization of the famed Rogers-Ramanujan partition identities. When viewed as q-series, these series can be connected to irreducible characters from vertex operator algebra theory. Then, when combined with standard tools from modular forms, we see that the Wronskians of these series satisfy nice modularity properties.

Comments

Portions of this document were previously published in a journal article and made available on arXiv.org.

Orcid ID

http://orcid.org/0000-0001-6624-2625

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