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We define Jacobi forms with complex multiplication. Analogous to modularforms with complex multiplication, they are constructed from Hecke charactersof the associated imaginary quadratic field. From this construction we obtain aJacobi form which specializes to $\eta(\tau)^{26}$ which we present tohighlight an open question of Dyson and Serre. We give other examples andapplications of Jacobi forms with complex multiplication including constructingtheta blocks associated to elliptic curves with complex multiplication and newfamilies of congruences and cranks for certain partition functions.

Jacobi forms with CM and applications