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The a-number of maximal curves of third largest genus | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 2، دوره 3، شماره 1، اردیبهشت 2022، صفحه 11-16 اصل مقاله (353.49 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.20511.1069 | ||
| نویسندگان | ||
| Vahid Nourozi1؛ Saeed Tafazolian* 2 | ||
| 1Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran | ||
| 2IMECC/UNICAMP, R. Sergio Buarque de Holanda, 651, Cidade Universitaria, Zeferino Vaz, 13083-859, Campinas, SP, Brazil | ||
| چکیده | ||
| The $a$-number is an invariant of the isomorphism class of the p-torsion group scheme. In this paper, we compute a closed formula for the $a$-number of $y^q + y = x^{\frac{q+1}{3}}$ and $\sum_{t=1}^{s} y^{q/3^t}= x^{q+1}$ with $q = 3^s$ over the finite field $\mathbb{F}_{q^2}$ using the action of the Cartier operator on $H^0(\mathcal{C},\Omega^1)$. | ||
| کلیدواژه‌ها | ||
| $a$-number؛ Cartier operator؛ Super-singular Curves؛ Maximal Curves | ||
| مراجع | ||
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