Geodesic
Variations on the Theme of Solvability by Radicals
Informatics and Automation, Analysis and singularities. Part 2, Tome 259 (2007), pp. 86-105

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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. 
@article{TRSPY_2007_259_a6,
     author = {A. G. Khovanskii},
     title = {Variations on the {Theme} of {Solvability} by {Radicals}},
     journal = {Informatics and Automation},
     pages = {86--105},
     publisher = {mathdoc},
     volume = {259},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2007_259_a6/}
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A. G. Khovanskii. Variations on the Theme of Solvability by Radicals. Informatics and Automation, Analysis and singularities. Part 2, Tome 259 (2007), pp. 86-105. http://geodesic.mathdoc.fr/item/TRSPY_2007_259_a6/