Doctoral Dissertations

Orcid ID

Date of Award


Degree Type


Degree Name

Doctor of Philosophy



Major Professor

Marie Jameson

Committee Members

Luis Finotti, Shashikant Mulay, Michael Berry


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.


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

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