Collected Item: “The number of unimodular roots of some reciprocal polynomials”
Врста публикације
Рад у часопису
Верзија рада
објављена верзија
Језик рада
енглески
Аутор/и (Милан Марковић, Никола Николић)
Dragan Stankov
Наслов рада (Наслов - поднаслов)
The number of unimodular roots of some reciprocal polynomials
Наслов часописа
COMPTES RENDUS MATHEMATIQUE
Година издавања
2020
Сажетак на енглеском језику
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.
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.
Волумен/том или годиште часописа
vol. 358 br. 2, str. 159-168
Број часописа
vol. 358 br. 2, str. 159-168
ISSN број часописа
ISSN (electronic) : 1778-3569
Кључне речи на српском (одвојене знаком ", ")
Algebraic integer; the house of algebraic integer; maximal modulus; reciprocal polynomial; primitive polynomial, Schinzel-Zassenhaus conjecture; Mahler measure; method of least squares; cyclotomic polynomials
Кључне речи на енглеском (одвојене знаком ", ")
Algebraic integer; the house of algebraic integer; maximal modulus; reciprocal polynomial; primitive polynomial, Schinzel-Zassenhaus conjecture; Mahler measure; method of least squares; cyclotomic polynomials
УДК број
https://doi.org/10.5802/crmath.28
Шира категорија рада према правилнику МПНТ
M20
Ужа категорија рада према правилнику МПНТ
М23
Пројект у склопу кога је настао рад
174032
Степен доступности
Одложени приступ
Лиценца
All rights reserved
Формат дигиталног објекта
.pdf