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arXiv · 1804.07589

On the modular completion of certain generating functions

Kathrin Bringmann·Stephan Ehlen·Markus Schwagenscheidt
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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.

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Kathrin Bringmann, Stephan Ehlen, Markus Schwagenscheidt. 2018-04-20. On the modular completion of certain generating functions. https://arxiv.org/abs/1804.07589

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