The number of nonunimodular roots of a reciprocal polynomial
Објеката
- Тип
- Рад у часопису
- Верзија рада
- објављена верзија
- Језик
- енглески
- Креатор
- Dragan Stankov
- Извор
- Comptes rendus mathematique
- Издавач
- Elsevier France Editions Scientifiques et Medicales
- Датум издавања
- 2023
- Сажетак
-
We introduce a sequence Pd of monic reciprocal polynomials with integer coefficients having the central coefficients fixed as well as the peripheral coefficients. We prove that the ratio of the number of nonunimodular roots of Pd to its degree d has a limit L when d tends to infinity. We show that if the coefficients of a polynomial can be arbitrarily large in modulus then L can be arbitrarily close to 0. It seems reasonable to believe that if the coefficients are bounded then the analogue of Lehmer’s Conjecture is true: either L=0 or there exists a gap so that L could not be arbitrarily close to 0. We present an algorithm for calculating the limit ratio and a numerical method for its approximation.
We estimated the limit ratio for a family of polynomials deduced from the powers of a given Salem number. We calculated the limit ratio of polynomials correlated to many bivariate polynomials having small Mahler measure introduced by Boyd and Mossinghoff. - том
- 361
- Број
- -
- почетак странице
- 423
- крај странице
- 435
- doi
- 10.5802/crmath.422
- issn
- 1631-073X
- 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
- Отворени приступ
- Лиценца
- All rights reserved
- Формат
- Медија
LimitRatioV4.pdf
Dragan Stankov. "The number of nonunimodular roots of a reciprocal polynomial" in Comptes rendus mathematique, Elsevier France Editions Scientifiques et Medicales (2023). https://doi.org/10.5802/crmath.422
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