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Variations on the theme of solvability by radicals

  • A. G. KhovanskiiEmail author
Article
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Abstract

We discuss the problem of representability and nonrepresentability of algebraic functions by radicals. We show that the Riemann surfaces of functions that are the inverses of Chebyshev polynomials are determined by their local behavior near branch points. We find lower bounds on the degrees of equations to which sufficiently general algebraic functions can be reduced by radicals. We also begin to classify rational functions of prime degree whose inverses are representable by radicals.

Keywords

Riemann Surface STEKLOV Institute Branch Point Prime Number Arithmetic Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  1. 1.University of TorontoCanada
  2. 2.Independent University of MoscowMoscowRussia
  3. 3.Institute of Systems AnalysisRussian Academy of SciencesMoscowRussia

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