The number of Weierstrass
points on a compact Riemann surface of finite genus g is at most (g − 1)g(g + 1) and
at least 2(g + 1). After the Riemann-Roch’s theorem for the class of canonical
semi-exact differentials, Watanabe considered the number of Weierstrass points on an
open Riemann surface of class OKD. In this paper it will be shown that
Watanabe’s estimate can be proved without any conception of principal
operators.