Prime form

In algebraic geometry, the Schottky–Klein prime form E(x,y) of a compact Riemann surface X depends on two elements x and y of X, and vanishes if and only if x = y.

Prime forms were introduced by Friedrich Schottky and Felix Klein.

Prime forms can be used to construct meromorphic functions on X with given poles and zeros.

If Σniai is a divisor linearly equivalent to 0, then ΠE(x,ai)ni is a meromorphic function with given poles and zeros.

This Riemannian geometry-related article is a stub.