Estimations de produits de polynômes. (Estimates of products of polynomials)
type: Item
instance of: scholarly article
title: Estimations de produits de polynômes. (Estimates of products of polynomials)
zbMATH Open document ID: 0578.30004
DOI: 10.1016/0022-314X(85)90062-9
published in: Journal of Number Theory
publication date: 1985-01-01T00:00:00Z
review text: Let \(P(z)=\sum_{j\geq 0}a_ jz^ j\) be a polynomial. Let \(P|^ k=\sum^{k}_{j=0}a_ jz^ j\). A typical result of this paper is the following: If \[ \| P\|_ 2=(\int | P(e^{i\theta})|^ 2(d\theta /2\pi))^{1/2}=1 \] and \(\| P|^ k\|_ 2\geq \delta >0\), then \[ \int^{2\pi}_{0}Log| P(e^{i\theta})| d\theta /2\pi \geq 2 Log(\delta /e\cdot 3^{k+1}). \] Some results pertain to the product of two polynomials.
Mathematics Subject Classification ID: 30C10
zbMATH DE Number: 3925188
zbMATH Keywords: product of polynomials
author: Bernard Beauzamy
author: Per Enflo
MaRDI profile type: Publication
cites work: Q5187492
cites work: Q3711161
cites work: Q4108810
cites work: On a Problem of Sidon in Additive Number Theory, and on some Related Problems
cites work: Nombres transcendants
full work available at URL: 0022-314x(85)90062-9
OpenAlex ID: W1990648410
description: scientific article; zbMATH DE number 3925188