On Zeros of Polynomials with Restricted Coefficients
نویسندگان
چکیده
منابع مشابه
On the Zeros of Polynomials with Restricted Coefficients
It is proved that a polynomial p of the form
متن کاملPolynomials with integer coefficients and their zeros
We study several related problems on polynomials with integer coefficients. This includes the integer Chebyshev problem, and the Schur problems on means of algebraic numbers. We also discuss interesting applications to the approximation by polynomials with integer coefficients, and to the growth of coefficients for polynomials with roots located in prescribed sets. The distribution of zeros for...
متن کاملMarkov Inequalities for Polynomials with Restricted Coefficients
Essentially sharp Markov-type inequalities are known for various classes of polynomials with constraints including constraints of the coefficients of the polynomials. For N and δ > 0 we introduce the class Fn,δ as the collection of all polynomials of the form P x ∑n k h akx k , ak ∈ Z, |ak | ≤ n , |ah| maxh≤k≤n|ak |. In this paper, we prove essentially sharp Markov-type inequalities for polynom...
متن کاملOn a problem of Byrnes concerning polynomials with restricted coefficients
We consider a question of Byrnes concerning the minimal degree n of a polynomial with all coefficients in {−1, 1} which has a zero of a given order m at x = 1. For m ≤ 5, we prove his conjecture that the monic polynomial of this type of minimal degree is given by ∏m−1 k=0 (x 2 − 1), but we disprove this for m ≥ 6. We prove that a polynomial of this type must have n ≥ e √ m(1+o(1)), which is in ...
متن کاملDistribution of zeros of polynomials with positive coefficients
We describe the limit zero distributions of sequences of polynomials with positive coefficients. MSC Primary: 30C15, 26C10, secondary: 31A05.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kyungpook mathematical journal
سال: 2015
ISSN: 1225-6951
DOI: 10.5666/kmj.2015.55.4.807