Date of Award
Doctor of Philosophy
Marie Jameson, Luis Finotti, Shashikant Mulay, Michael Langston
We begin with an overview of the theory of modular forms as well as some relevant sub-topics in order to discuss three results: the first result concerns positivity of self-conjugate t-core partitions under the assumption of the Generalized Riemann Hypothesis; the second result bounds certain types of congruences called "Ramanujan congruences" for an infinite class of eta-quotients - this has an immediate application to a certain restricted partition function whose congruences have been studied in the past; the third result strengthens a previous result that relates weakly holomorphic modular forms to newforms via p-adic limits.
Hanson, Michael Anthony, "Coefficients of modular forms and applications to partition theory. " PhD diss., University of Tennessee, 2023.