An algorithm for constructing certain differential operators in positive characteristic

  • Alberto F. Boix
  • Alessandro De Stefani
  • Davide Vanzo
Keywords: Algorithm, Differential operator, Frobenius map, Prime characteristic


Given a non-zero polynomial f in a polynomial ring R with coefficients in a finite field of prime characteristic p, we present an algorithm to compute a differential operator δ which raises 1/ f to its pth power. For some specific families of polynomials, we also study the level of such a differential operator δ , i.e., the least integer e such that δ is R^{p^e} -linear. In particular, we obtain a characterization of supersingular elliptic curves in terms of the level of the associated differential operator.