Modularity of Taylor coefficients of non-holomorphic Jacobi forms arising from partitions

It is well-known that Taylor coefficient of holomorphic Jacobi forms is quasimodular forms, and recently it was proved by Bringmann that such a property still holds for certain non-holomorphic Jacobi forms arising in combinatorics. In this paper, we prove further modularity results of an infinite family of combinatorial sums related to non-holomorphic Jacobi forms. More precisely, for each k >= 2 and & ell; >= 1 we find non-holomorphic modular forms r(2 & ell; -1,k)(tau) arising from partitions. It turns out that the non-holomorphic part of r(1,k)(tau) is related to the generalized Rogers-Ramanujan functions. This appearance of generalized Rogers-Ramanujan functions is supported by the fact that this r(1,k)(tau) is a mixed harmonic Maass form. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.