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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 259, Pages 86–105 (Mi tm571)  
This article is cited in 4 scientific papers (total in 4 papers)

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
Full-text PDF (280 kB) Citations (4)
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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.
Received in December 2006
English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 259, Pages 82–100
DOI: https://doi.org/10.1134/S0081543807040074
Bibliographic databases:
UDC: 512.62+512.12
Language: Russian
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, Trudy Mat. Inst. Steklova, 259, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 86–105; Proc. Steklov Inst. Math., 259 (2007), 82–100
Citation in format AMSBIB
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\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 Trudy 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://mathscinet.ams.org/mathscinet-getitem?mr=2433679}
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\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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