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Uniformisation of algebraic curves: on the Burnside curve

Monday 19th November 2001 - 15:00 to 16:00
INI Seminar Room 2
We draw attention to the first and only example of an algebraic curve of genus g>1 (the Burnside curve) which has a complete parametrisation in terms of known special functions. As a byproduct of our consideration we get accessory parameters for the associated Fuchsian equation, its complete integral, and a few little-known formulas in the theory of Weierstrass elliptic functions and series expansions for the meromorphic functions, parametrizing the Burnside curve.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons