| Let H=N,c M12 N,c be the space of Hilbert modular forms of half integral weight of all levels N and characters chi.; We denote by 4N: OF→C a periodic function of period N . Let theta be the C-linear space of the functions f : HxH→ C , fz= tx∈OF 4Nt x exptpi x2z1+x '2z2 where, for each f, t ∈ OF runs through a finite subset of totally positive integers of F.; Main theorem. H=Q; Using this theorem, for some fixed F's, an explicit basis can be found. Some examples are given in Chapter 4. |
