Abstract

Let M#k(52) be the space of weight k level 52 weakly holomorphic modular forms with poles only at infinity, and S#k(52) the subspace of forms which vanish at all cusps other than infinity. For these spaces we construct canonical bases, indexed by the order of vanishing at infinity. We prove that the coefficients of the canonical basis elements satisfy a duality property. Further, we give closed forms for the generating functions of these basis elements.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2017-07-01

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd9422

Keywords

modular forms, Zagier duality, weakly holomorphic

Included in

Mathematics Commons

Share

COinS