Sur le diamètre transfini entier d'un intervalle réel. (On the transfinite integer diameter of a real interval)
type: Item
instance of: scholarly article
title: Sur le diamètre transfini entier d'un intervalle réel. (On the transfinite integer diameter of a real interval)
zbMATH Open document ID: 0713.41004
author: Francesco Amoroso
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74904
review text: Let \(X\subset C\) be a compact set; its transfinite integer diameter \(t_ Z(X)\) is defined as a measure for the least deviation from zero of integral polynomials over X. The behaviour of the function \(t_ Z\) over the set of all intervals I is studied. In particular, some bounds for \(t_ Z(I)\) which become sharp for intervals with rational extremities, are given. These bounds, obtained combining the theory of orthogonal polynomials with elementary arguments from the geometry of numbers, explicitly depend on the diameter of I and on the denominators of its extremities.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 4173583
zbMATH Keywords: transfinite integer diameter
MaRDI profile type: Publication
OpenAlex ID: W2323963472
cites work: Q4485496
cites work: Q3338332
cites work: Q3882893
cites work: Q3834142
cites work: Q3834141
cites work: On Chebyshev-Type Inequalities for Primes
cites work: A New Method in Elementary Prime Number Theory
cites work: Q5639997
DOI: 10.5802/AIF.1240
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4173583