Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms

Jan-Willem van Ittersum, Georg Oberdieck, Aaron Pixton

Published 2020-07-07Version 1

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.