The Bloch-Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms
arXiv:2102.12964 · doi:10.1007/s40687-022-00369-5
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.
Final version; to appear in Res. Math. Sci