Prime form and sigma function

John Gibbons, Shigeki Matsutani, Yoshihiro Onishi

In this article, we study some cyclic $(r,s)$ curves $X$ given by $y^r=x^s+{\lambda }_1{x}^{s-1}+...+{\lambda }_{s-1}x+{\lambda }_s$. We give an expression for the prime form $\cE(P,Q)$, where $(P,…