The Construction of Automorphic Forms from the Derivatives of a Given Form

Let f(z) be a meromorphic automorphic form of real or complex dimension - k belonging to the horocyclic [2] group Γ (Fuchsian group of the first kind, Grenzkreisgruppe), and furnished with a multiplier system v. We write thisf(z) ∈ {Γ, k, v}, and denote by v^r, for integral r, the multiplier system which is the rth power of v.