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arXiv · 2102.12964

The Bloch-Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms

Jan-Willem M. van Ittersum
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Abstract

There are many families of functions on partitions, such as the shifted symmetric functions, for which the corresponding q-brackets are quasimodular forms. We extend these families so that the corresponding q-brackets are quasimodular for a congruence subgroup. Moreover, we find subspaces of these families for which the q-bracket is a modular form. These results follow from the properties of Taylor coefficients of strictly meromorphic quasi-Jacobi forms around rational lattice points.

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Jan-Willem M. van Ittersum. 2021-02-25. The Bloch-Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms. https://doi.org/10.1007/s40687-022-00369-5

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