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KIAM Preprint № 13, Moscow, 2007
Authors: Aptekarev A. I., Lysov V. G., Tulyakov D. N.
Three-sheeted Riemann surfaces of genus 0 with fixed projections of the branch points
New constructive procedures for determination of the equations for the algebraic functions of the third order and of genus zero are proposed. We discovered that there exist four types of the Riemann surfaces for these functions, which are distinguished by the groups of permutations of the sheets in the branch points. Using the coefficients of the equations we compute the extremal cuts of the Riemann surfaces. These cuts are the attractive sets for the poles of the Hermite--Pade approximants.
Publication language: russian,  pages: 21
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Aptekarev Alexander Ivanovich, RAS
  • Lysov Vladimir Genrikhovich,  KIAM RAS
  • Tulyakov Dmitriy Nikolaevich,  KIAM RAS