Abstract

Let M_k^(∞) (Gamma, nu) denote the space of weight k weakly holomorphic weight modular forms with poles only at the cusp (∞), and let widehat M_k^(∞) (Gamma, nu) subseteq M_k^(∞) (Gamma, nu) denote the space of weight k weakly holomorphic modular forms in M_k^(∞) (Gamma, nu) which vanish at every cusp other than (∞). We construct canonical bases for these spaces in terms of Maass--Poincaré series, and show that the coefficients of these bases satisfy Zagier duality.

Degree

College and Department

Physical and Mathematical Sciences; Mathematics

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