Department of Mathematics and Statistics,
Concordia University,
7141 Sherbrooke West,
Montreal H4BIR6,
Montreal PQ, CANADA
Institute of Magnetism of NAS of Ukraine,
36-b Vernadskii Ave.,
03142 Kyiv, UKRAINE

Symmetric monopoles and identity of Ramanujan

We develop the Ercolani-Sinha constrains of $SU(2)$ monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles.  In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of curve with $Z_N$ symmetry the transendental constraints become a number theoretic problem and a recently proven identity of Ramanujan provides a solution. The Ercolani-Sinha constraints provides a gauge-transform of the Nahm data.