Degree Name

Department

Mathematics

College

Physical and Mathematical Sciences

Defense Date

2018-11-12

Publication Date

2018-11-29

First Faculty Advisor

Paul Jenkins

First Faculty Reader

Pace Nielsen

Second Faculty Reader

Michael Griffin

Honors Coordinator

Paul Jenkins

Keywords

modular forms, congruence, duality, canonical bases

Abstract

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

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