Polynomials invertible in k-radicals

Yuri Burda; Askold Khovanskii

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arXiv · 1209.5137

Polynomials invertible in k-radicals

Yuri Burda·Askold Khovanskii

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Abstract

A classic result of Ritt describes polynomials invertible in radicals: they are compositions of power polynomials, Chebyshev polynomials and polynomials of degree at most 4. In this paper we prove that a polynomial invertible in radicals and solutions of equations of degree at most k is a composition of power polynomials, Chebyshev polynomials, polynomials of degree at most k and, if k < 15, certain polynomials with exceptional monodromy groups. A description of these exceptional polynomials is given. The proofs rely on classification of monodromy groups of primitive polynomials obtained by Müller based on group-theoretical results of Feit and on previous work on primitive polynomials with exceptional monodromy groups by many authors.

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Yuri Burda, Askold Khovanskii. 2012-09-24. Polynomials invertible in k-radicals. https://arxiv.org/abs/1209.5137

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