An algorithm for constructing certain differential operators in positive 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 differenti...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
2015-05-01
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| Series: | Le Matematiche |
| Subjects: | |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1237 |
| _version_ | 1818147133845405696 |
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| author | Alberto F. Boix Alessandro De Stefani Davide Vanzo |
| author_facet | Alberto F. Boix Alessandro De Stefani Davide Vanzo |
| author_sort | Alberto F. Boix |
| collection | DOAJ |
| description | 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.<br /><br /> |
| first_indexed | 2024-12-11T12:30:24Z |
| format | Article |
| id | doaj.art-56abe06796d14f8c94a41d948bd5e8af |
| institution | Directory Open Access Journal |
| issn | 0373-3505 2037-5298 |
| language | English |
| last_indexed | 2024-12-11T12:30:24Z |
| publishDate | 2015-05-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| series | Le Matematiche |
| spelling | doaj.art-56abe06796d14f8c94a41d948bd5e8af2022-12-22T01:07:15ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982015-05-01701239271941An algorithm for constructing certain differential operators in positive characteristicAlberto F. BoixAlessandro De StefaniDavide VanzoGiven 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.<br /><br />http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1237AlgorithmDifferential operatorFrobenius mapPrime characteristic |
| spellingShingle | Alberto F. Boix Alessandro De Stefani Davide Vanzo An algorithm for constructing certain differential operators in positive characteristic Le Matematiche Algorithm Differential operator Frobenius map Prime characteristic |
| title | An algorithm for constructing certain differential operators in positive characteristic |
| title_full | An algorithm for constructing certain differential operators in positive characteristic |
| title_fullStr | An algorithm for constructing certain differential operators in positive characteristic |
| title_full_unstemmed | An algorithm for constructing certain differential operators in positive characteristic |
| title_short | An algorithm for constructing certain differential operators in positive characteristic |
| title_sort | algorithm for constructing certain differential operators in positive characteristic |
| topic | Algorithm Differential operator Frobenius map Prime characteristic |
| url | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1237 |
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