Numerical semigroups which cannot be realized as semigroups of Galois Weierstrass points

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Morrison and Pinkham [4] gave a characterization of the semigroups of Galois Weierstrass points, i.e., total ramification points of cyclic coverings of the projective line of degree n. They showed that such a semigroup must satisfy certain equalities, which we call the M-P equalities in this paper, and that the converse holds for any prime \(n\leqq 7\). In this paper we consider the case when n is a prime number \(p \geqq 11\). For each prime \(p \geqq 11\), we give a semigroup which satisfies the M-P equalities but is not the semigroup of a Galois Weierstrass point. For this, we study the semigroups of Galois Weierstrass points using the equations defining curves which are cyclic covering of the projective line.