The number of unimodular roots of some reciprocal polynomials

Објеката

Тип
Рад у часопису
Верзија рада
објављена верзија
Језик
енглески
Креатор
Dragan Stankov
Извор
Cmptes rendus mathematique
Датум издавања
2020
Сажетак
We introduce a sequence P2n of monic reciprocal polynomials with integer coefficients having the central coefficients fixed. We prove that the ratio between number of nonunimodular roots of P2n and its degree d has a limit when d tends to infinity. We present an algorithm for calculation the limit and a numerical
method for its approximation. If P2n is the sum of a fixed number of monomials we determine the central coefficients such that the ratio has the minimal limit. We generalise the limit of the ratio for multivariate polynomials. Some examples suggest a theorem for polynomials in two variables which is analogous to Boyd’s
limit formula for Mahler measure.
том
358
Број
2
почетак странице
159
крај странице
168
doi
10.5802/crmath.28
issn
1778-3569
Subject
Algebraic integer, the house of algebraic integer, maximal modulus, reciprocal polynomial, primitive polynomial, Schinzel-Zassenhaus conjecture, Mahler measure, method of least squares, cyclotomic polynomials
Шира категорија рада
M20
Ужа категорија рада
М23
Је дио
174032
Права
Одложени приступ
Лиценца
All rights reserved
Формат
.pdf
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Драган Станков
Radovi istraživača

Dragan Stankov. "The number of unimodular roots of some reciprocal polynomials" in Cmptes rendus mathematique (2020). https://doi.org/10.5802/crmath.28

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