The $a$-number of maximal curves of third largest genus

Document Type : Original Article

Authors

1 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

2 IMECC/UNICAMP, R. Sergio Buarque de Holanda, 651, Cidade Universitaria, Zeferino Vaz, 13083-859, Campinas, SP, Brazil

Abstract

‎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 $H^0(mathcal{C},Omega^1)$‎.

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