On the modular completion of certain generating functions
Abstract
We complete several generating functions to non-holomorphic modular forms in two variables. For instance, we consider the generating function of a natural family of meromorphic modular forms of weight two. We then show that this generating series can be completed to a smooth, non-holomorphic modular form of weights 3/2 and two. Moreover, it turns out that the same function is also a modular completion of the generating function of weakly holomorphic modular forms of weight 3/2, which prominently appear in work of Zagier on traces of singular moduli.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.07589
- arXiv:
- arXiv:1804.07589
- Bibcode:
- 2018arXiv180407589B
- Keywords:
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- Mathematics - Number Theory;
- 11F37;
- 11F27
- E-Print:
- 26 pages