Physical and Mathematical Sciences
First Faculty Advisor
First Faculty Reader
Second Faculty Reader
modular forms, congruence, duality, canonical bases
We prove divisibility results for the Fourier coefficients of canonical basis elements for the spaces of weakly holomorphic modular forms of weight 0 and levels 6, 10, 12, 18 with poles only at the cusp at infinity. In addition, we show that these Fourier coefficients satisfy Zagier duality in all weights, and give a general formula for the generating functions of such canonical bases for all genus zero levels. These results originally appeared in a paper of the same title that was accepted by the journal Integers, and was authored by the present author, with Paul Jenkins and Vicki
BYU ScholarsArchive Citation
Warnick, Merrill, "Divisibility Properties of Coefficients of Modular Functions of Genus Zero Levels" (2018). Undergraduate Honors Theses. 51.