Higher-order Weierstrass Weights of Branch Points on Superelliptic Curves
نویسندگان
چکیده
In this paper we consider the problem of calculating the higherorder Weierstrass weight of the branch points of a superelliptic curve C. For any q > 1, we give an exact formula for the q-weight of an affine branch point. We also find a formula for the q-weight of a point at infinity in the case where n and d are relatively prime. With these formulas, for any fixed n, we obtain an asymptotic formula for the ratio of the q-weight of the branch points, denoted BWq , to the total q-weight of points on the curve: lim inf d→∞ BWq g(g − 1)(2q − 1) ≥ n+ 1 3(n− 1)(2q − 1) , with equality when the limit is taken such that gcd(n, d) = 1.
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