An algorithm for constructing certain differential operators in positive characteristic
Keywords:
Algorithm, Differential operator, Frobenius map, Prime characteristicAbstract
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.Downloads
Published
Issue
Section
License
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
