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.
| Identifer | oai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-7990 |
| Date | 01 July 2018 |
| Creators | Molnar, Grant Steven |
| Publisher | BYU ScholarsArchive |
| Source Sets | Brigham Young University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Theses and Dissertations |
| Rights | http://lib.byu.edu/about/copyright/ |
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