Variations on the theme of solvability by radicals |
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Authors: | A. G. Khovanskii |
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Affiliation: | (1) University of Toronto, Ontario, M5S 2E4, Canada;(2) Independent University of Moscow, Bol’shoi Vlas’evskii per. 11, Moscow, 119002, Russia;(3) Institute of Systems Analysis, Russian Academy of Sciences, pr. 60-letiya Oktyabrya 9, Moscow, 117312, Russia |
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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. Original Russian Text ? A.G. Khovanskii, 2007, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 259, pp. 86–105. To Vladmir Igorevich Arnold, mathematical idol of my generation |
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