Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve

Abstract

In this paper we determine the generalized Weierstrass semigroup $\hat{H}(P_{\infty },P_1,\dots ,P_m)$, and consequently the Weierstrass semigroup $H(P_{\infty },P_1,\dots ,P_m)$, at $m+1$ points on the curves ${\mathcal{X}}_{a,b,n,s}$ and ${\mathcal{Y}}_{n,s}$. These curves has been introduced in Tafazolian et al. as new examples of curves which cannot be covered by the Hermitian curve.