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...
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Università degli Studi di Catania
2015-05-01
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| Series: | Le Matematiche |
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| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1237 |
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doaj-56abe06796d14f8c94a41d948bd5e8af2020-11-25T03:37:36ZengUniversità 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Alberto F. Boix Alessandro De Stefani Davide Vanzo |
| 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 |
| author_facet |
Alberto F. Boix Alessandro De Stefani Davide Vanzo |
| author_sort |
Alberto F. Boix |
| title |
An algorithm for constructing certain differential operators in positive characteristic |
| title_short |
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_sort |
algorithm for constructing certain differential operators in positive characteristic |
| publisher |
Università degli Studi di Catania |
| series |
Le Matematiche |
| issn |
0373-3505 2037-5298 |
| publishDate |
2015-05-01 |
| 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 /> |
| topic |
Algorithm Differential operator Frobenius map Prime characteristic |
| url |
http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1237 |
| work_keys_str_mv |
AT albertofboix analgorithmforconstructingcertaindifferentialoperatorsinpositivecharacteristic AT alessandrodestefani analgorithmforconstructingcertaindifferentialoperatorsinpositivecharacteristic AT davidevanzo analgorithmforconstructingcertaindifferentialoperatorsinpositivecharacteristic AT albertofboix algorithmforconstructingcertaindifferentialoperatorsinpositivecharacteristic AT alessandrodestefani algorithmforconstructingcertaindifferentialoperatorsinpositivecharacteristic AT davidevanzo algorithmforconstructingcertaindifferentialoperatorsinpositivecharacteristic |
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