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

Jan-Willem M. van Ittersum

Published 2021-02-25Version 1

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.