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
.pdf
Скупови објеката
Драган Станков
Radovi istraživača
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

This item was submitted on 24. јануар 2023. by [anonymous user] using the form “Рад у часопису” on the site “Радови”: http://romeka.rgf.rs/s/repo

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