International Mathematics Research Notices ( IF 1.452 ) Pub Date : 2020-01-11 , DOI: 10.1093/imrn/rnz338
Bringmann K, Ehlen S, Schwagenscheidt M.

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 $\frac 32$ 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 $\frac 32$, which prominently appear in work of Zagier [ 27] on traces of singular moduli.

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