FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1123-1145

Generalized Chebyshev polynomials and Pell--Abel equation

A. V. Pastor

Abstract

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In this paper the question of the compositional reducibility of generalized Chebyshev polynomials is solved by studying the combinatorial structure of plane trees. As a particular case we deduce the criterion of minimality of the solution of Pell--Abel equation corresponding to a given plane tree. Some other applications are also considered.

All articles are published in Russian.

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Last modified: April 17, 2002