Victor Enolski

To the existence of charge 3 monopole: theta-functional approach

The
Ercolani-Sinha construction of $SU(2)$ monopoles is developed and made effective for charge 3
monopoles. It is shown how to solve the
transcendental constraints arising on the spectral curve.
For a class of symmetric curves the transcendental constraints become a number theoretic problem and a recently proven identity of Ramanujan provides a solution. One-parametric family of charge 3 monopole curves that includes thetrahedral monopole is decribed by means of theta-functions.