Hecke operators on differential modular forms mod p

A description is given of all primitive delta-series mod p of order 1 which are eigenvectors of all the Hecke operators nT(kappa)(n), "pT(kappa)(p)", (n, p) = 1, and which are delta-Fourier expansions of delta-modular forms of arbitrary order and weight w with deg(w) = kappa >= 0; this set of delta-series is shown to be in a natural one-to-one correspondence with the set of series mod p (of order 0) which are eigenvectors of all the Hecke operators T kappa+2(n), T kappa+2(p) (n, p) = 1 and which are Fourier expansions of (classical) modular forms of weight equivalent to kappa + 2 mod p - 1. (C) 2012 Elsevier Inc. All rights reserved.