EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 97(111), pp. 57–67 (2015)

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Dragan Stankov

Katedra Matematike RGF-a, University of Belgrade, Belgrade, Serbia

Abstract: We investigate an infinite sequence of polynomials of the form: $$ a_0T_n(x)+a_1T_{n-1}(x)+\dots+a_mT_{n-m}(x) $$ where $(a_0,a_1,\ldots,a_m)$ is a fixed $m$-tuple of real numbers, $a_0,a_m\neq0$, $T_i(x)$ are Chebyshev polynomials of the first kind, $n=m,m+1,m+2,\ldots$ Here we analyze the structure of the set of zeros of such polynomial, depending on $A$ and its limit points when $n$ tends to infinity. Also the expression of envelope of the polynomial is given. An application in number theory, more precise, in the theory of Pisot and Salem numbers is presented.

Keywords: Chebyshev polynomials, envelope, Pisot numbers, Salem numbers

Classification (MSC2000): 11B83; 11R09;12D10

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Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.

© 2015 Mathematical Institute of the Serbian Academy of Science and Arts
© 2015 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition