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

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

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