cl(JacC) corresponding to each isomorphy class of a (smooth) curve the isomorphy class of its canonically polarized Jacobian variety J ac C = (J( C), Ec).
Therefore also r (yC3) has six generators, say gl, ... ,g6. They have been explicitly described already by PICARD  (with correction in ) and ALEZAIS. Their symplectic lifts Gi = *gi E §p(6, Z), i = 1, ... 50). 28 (i), (iii) for suitable holomorphic functions th on lB it is sufficient to check them for the generators of r( yC3). According to our claim th = Thba we have now only to look for holomorphic functions T h on H3 satisfying the six restricted functional equations Th 0 Gi = (detg;)2.
Qr dx/yi, ... 21). 22 (). 1 coincides with the left ideal sheaf of differential operators killing the hypergeometric integral functions 10 , ... 22). 10) with w instead of F one can take the family of PICARD curves and w represented by the differential form w = dx/y depending on u, v. Taking integrals along cycles one gets an "algebraic" fundamental system of solutions J h(t) = w(t), k=O,1,2, t=(U,V)Ejp'2\~J, w=dx/y. 10) in an explicit and algebraic manner. 23. 10) along linearly independent cycle families Qo(t), Ql (t), & Q2(t).