The sixth Painleve transcendent and uniformization of algebraic curves - Mathematics > Classical Analysis and ODEsReportar como inadecuado




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Abstract: We exhibit a remarkable connection between sixth equation of Painleve listand infinite families of explicitly uniformizable algebraic curves. Fuchsianequations, congruences for group transformations, differential calculus offunctions and differentials on corresponding Riemann surfaces, Abelianintegrals, analytic connections generalizations of Chazy-s equations, andother attributes of uniformization can be obtained for these curves. Asbyproducts of the theory, we establish relations between Picard-Hitchin-scurves, hyperelliptic curves, punctured tori, Heun-s equations, and the famousdifferential equation which Apery used to prove the irrationality of Riemann-szeta3.



Autor: Yurii V. Brezhnev

Fuente: https://arxiv.org/







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