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 yq + ‎y =x(q+1)/3 and  $sum_{t=1}^{s} y^{q⁄ 3^t}= xq+1$ with q = 3s over the finite field‎ ‎Fq2 using the action of the Cartier operator on H0(C1).

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