The hyperelliptic p-function

Abstract

On any hyperelliptic jacobian Jac C, there is one meromorphic function which is most important, playing a central role in the function theory on Jac C. When g = 1, this function is Weierstrass’ p-function, so, at the risk of precipitating some confusion in notation, we want to call this function $\mathfrak{p}\left( {\vec z} \right)$ too.