Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms - Ittersum, Jan-Willem van; Oberdieck, Georg; Pixton, Aaron C. (Selecta mathematica, 2021)
We prove the existence of quasi-Jacobi form solutions for an analogue of the Kaneko-Zagier differential equation for Jacobi forms. The transformation properties of the solutions under the Jacobi group are derived. A special feature of the solutions is the polynomial dependence of the index parameter. The results yield an explicit conjectural description for all double ramification cycle integrals in the Gromov-Witten theory of K3 surfaces.