On Weierstrass Semigroups of Some Triples on Norm-Trace Curves

摘要

In this paper, we consider the norm-trace curves which arerndefined by the equation y~(q~(r-1)) + y~((r-2)) + ... + y = x (q~r-1)/(q-1) over IF_(q~r) where q is a power of a prime number and r ≥ 2 is an integer. We determine the Weierstrass semigroup of the triple of points (P_∞,P_(00),P_(0b)) on this curve.