Jacobi modular forms on subgroups of the modular group

摘要

Let Ek(τ) and Ek,m(z,τ) be the Eisenstein series of weight k and, weight k and index m. H is the complex upper half plane. φ/k,m∈Jk,m(Γ) is a Jacobi modular form of weight k and index m for the congruence subgroup Γ≅PSL(2,Z) in generated by the elements U=0−110 and V=1101. E4veEk,m are generators of the space of Jacobi forms. In this paper, we express the Weierstrass ℘(z,τ) function as a rational function of φ12,1 and φ10,1, and defined by G(z,τ)=φ12,1(z,τ)/φ10,1(z,τ). Then two theorems are constructed.