In algebraic geometry, the SchottkyâÂÂKlein 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. The prime form E is not quite a holomorphic function on X àX, but is a section of a holomorphic line bundle over this space. 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 ãn<sub>i</sub>a<sub>i</sub> is a divisor linearly equivalent to 0, then àE(x,a<sub>i</sub>)<sup>n<sub>i</sub></sup> is a meromorphic function with given poles and zeros.