Weierstrass points of the Fermat curve

Abstract

Let R denote a compact Riemann surface of genus g ≥ 2. A point P on R is called a Weierstrass point if there exists a meromorphic function on R which has a pole of order less than or equal to g at P and holomorphic elsewhere. The set of Weierstrass points is nonempty and finite. This result is due to Hurwitz[3].