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Painleve I, Coverings of the Sphere and Belyi Functions (1207.4361v2)
Published 18 Jul 2012 in math-ph, math.CA, and math.MP
Abstract: The theory of poles of solutions of Painleve-I is equivalent to the Nevanlinna problem of constructing a meromorphic function ramified over five points - counting multiplicities - and without critical points. We construct such meromorphic functions as limit of rational ones. In the case of the tritronquee solution these rational functions are Belyi functions.
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