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
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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