TY - JOUR
ID - 4553
TI - The $a$-number of maximal curves of third largest genus
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Nourozi, Vahid
AU - Tafazolian, Saeid
AD - Faculty of Mathematics and Computer Science‎, ‎Amirkabir University of Technology
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
Y1 - 2021
PY - 2021
VL -
IS -
SP -
EP -
KW - $a$-number
KW - Cartier operator
KW - Super-singular Curves
KW - Maximal Curves
DO - 10.22060/ajmc.2021.20511.1069
N2 - 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 $H^0(mathcal{C},Omega^1)$.
UR - https://ajmc.aut.ac.ir/article_4553.html
L1 -
ER -