A generalized Kiepert formula for Cab curves

被引：0
作者：
Shigeki Matsutani
Emma Previato
机构：
[1] 8-21-1 Higashi-Linkan,Institut Mittag
[2] The Royal Swedish Academy of Sciences,Leffer
[3] Boston University,Department of Mathematics and Statistics
来源：
Israel Journal of Mathematics | 2009年 / 171卷
关键词：
Riemann Surface; Elliptic Curve; Compact Riemann Surface; Hyperelliptic Curve; Weierstrass Point;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Kiepert (1873) and Brioschi (1864) published algebraic equations for the n-division points of an elliptic curve, in terms of the Weierstrass ℘-function and its derivatives with respect to a uniformizing parameter, or another elliptic function, respectively. We generalize both types of formulas for a compact Riemann surface which, outside from one point, has a smooth polynomial equation in the plane, in the sense that we characterize the points whose n-th multiple in the Jacobian belongs to the theta divisor.
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页码：305 / 323
页数：18
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