The $a$-number of maximal curves of third largest genus
نویسندگان
1 Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran
2 IMECC/UNICAMP, R. Sergio Buarque de Holanda, 651, Cidade Universitaria, Zeferino Vaz, 13083-859, Campinas, SP, Brazil
doi
10.22060/ajmc.2021.20511.1069چکیده
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 $H^0(\mathcal{C},\Omega^1)$.
