On roots of polynomials with positive coefficients
نویسندگان
چکیده
منابع مشابه
Roots of polynomials with positive coefficients
We describe the limit zero distributions of sequences of polynomials with positive coefficients. We also characterize the polynomials with real coefficients for which some power has positive coefficients. MSC Primary: 30C15, 26C10, secondary: 31A05.
متن کاملOn continuous dependence of roots of polynomials on coefficients
It is a well know result that roots of a polynomial depend continuously on its coefficients. Here we review this basic result and produce a proof via the use of Rouché’s Theorem. We also provide a simple result regarding real simple roots of polynomials with real coefficients.
متن کاملCoefficients and Roots of Peak Polynomials
Given a permutation π = π1π2 · · ·πn ∈ Sn, we say an index i is a peak if πi−1 < πi > πi+1. Let P (π) denote the set of peaks of π. Given any set S of positive integers, define PS(n) = {π ∈ Sn : P (π) = S}. Billey-Burdzy-Sagan showed that for all fixed subsets of positive integers S and sufficiently large n, |PS(n)| = pS(n)2 for some polynomial pS(x) depending on S. They conjectured that the co...
متن کاملCoefficients and Roots of Ehrhart Polynomials
The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coefficients of Ehrhart polynomials and relate them to known inequalities. We also investigate the roots of Ehrhart polynomials. We prove that for fixed d, there exists a bounded region of C containing all roots of Ehrhart polynomials...
متن کاملHeights of roots of polynomials with odd coefficients
We show that the height of a non-zero non root of unity α which is the zero of a polynomial with all odd coefficients of degree n satisfies h(α) ≥ 0.4278 n+ 1 . More generally we obtain bounds when the coefficients are all congruent to 1 modulo m for some m ≥ 2.
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: Publications de l'Institut Mathematique
سال: 2011
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1103089z