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.
Recommended Citation
Wieczorek, Margaret Anne, "Modular forms, partitions, and q-series. " PhD diss., University of Tennessee, 2020.
https://trace.tennessee.edu/utk_graddiss/5924
Comments
Portions of this document were previously published in a journal article and made available on arXiv.org.