The $a$-number of jacobians of certain maximal curves

Abstract

In this paper, we compute a formula for the $a$-number of certain maximal curves given by the equation $y^{q}+y=x^{frac{q+1}{2}}$ over the finite field $mathbb{F}_{q^2}$. The same problem is studied for the maximal curve corresponding to $sum_{t=1}^s y^{q/2^t}=x^{q+1}$ with $q=2^s$, over the finite field $mathbb{F}_{q^2}$.