m at h . A G ] 1 9 Fe b 20 14 Weierstrass points on Kummer extensions

Let F be an algebraic function field in one variable defined over an algebraically closed field K of characteristic p ≥ 0. For any given place P of F , a number s is called a non-gap at P if there exists a function z ∈ F such that the pole divisor of z is (z)∞ = sP . If there is no such function, the number s is called a gap at P . If g is the genus of F , it follows from the Riemann-Roch theorem that there are exactly g gaps at any place P of F [19]. It is a well known fact that for all, but finitely many places P , the gap sequence (of g numbers) is always the same. This sequence is called the gap sequence of F . When the gap sequence of F is (1, 2, . . . , g), the sequence is called ordinary, and we say that the function field F is classical, otherwise F is called nonclassical. The places for which the gap sequence is not equal to the gap sequence of F are called Weierstrass.