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 Tr. Mat. Inst. Steklova, 2007, Volume 259, Pages 86–105 (Mi tm571)

Variations on the Theme of Solvability by Radicals

A. G. Khovanskiiabc

a Institute of Systems Analysis, Russian Academy of Sciences
b Independent University of Moscow
c University of Toronto

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 259, 82–100

Bibliographic databases:

UDC: 512.62+512.12

Citation: A. G. Khovanskii, “Variations on the Theme of Solvability by Radicals”, Analysis and singularities. Part 2, Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 259, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 86–105; Proc. Steklov Inst. Math., 259 (2007), 82–100

Citation in format AMSBIB
\Bibitem{Kho07} \by A.~G.~Khovanskii \paper Variations on the Theme of Solvability by Radicals \inbook Analysis and singularities. Part~2 \bookinfo Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday \serial Tr. Mat. Inst. Steklova \yr 2007 \vol 259 \pages 86--105 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm571} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2433679} \zmath{https://zbmath.org/?q=an:1182.30009} \elib{https://elibrary.ru/item.asp?id=9572730} \transl \jour Proc. Steklov Inst. Math. \yr 2007 \vol 259 \pages 82--100 \crossref{https://doi.org/10.1134/S0081543807040074} \elib{https://elibrary.ru/item.asp?id=13544502} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38849136705} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yuri Burda, Ascold Khovanskii, “Signatures of branched coverings and solvability in quadratures”, Mosc. Math. J., 14:2 (2014), 225–237
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