Let Mk(∞) (Gamma, nu) denote the space of weight k weakly holomorphic weight modular forms with poles only at the cusp (∞), and let widehat Mk(∞) (Gamma, nu) subseteq Mk(∞) (Gamma, nu) denote the space of weight k weakly holomorphic modular forms in Mk(∞) (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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Molnar, Grant Steven, "The Arithmetic of Modular Grids" (2018). Theses and Dissertations. 6990.
weakly holomorphic modular forms, harmonic Maass forms, Zagier duality, Bruinier-Funke pairing