A compendium of results in additive number theory
type: Item
instance of: scholarly article
title: A compendium of results in additive number theory
zbMATH Open document ID: 1373.11076
author: Luan Alberto Ferreira
published in: São Paulo Journal of Mathematical Sciences
publication date: 2015-09-25T00:00:00Z
review text: The author gives short overviews on selected classical results and problems in additive number theory. The titles of the sections are: additive basis; asymptotic additive basis; thin additive basis, asymptotic additive bases, Schirelmann density, Schnirelmann's and Mann's inequalities, essential components and Plünnecke's inequality, thin additive bases, other densities, van der Waerden's, Szemerédi's and Green-Tao's theorem, Pollock's conjectures, the exact solution of Waring's problem, the asymptotic Waring's problem, Erdős-Turán conjecture on asymptotic bases, the thin bases problem, the Goldbach's conjecture, van der Waerden's numbers and Erdős conjecture on arithmetic progressions. No proofs are provided, but the items are accompanied by at least one reference where a proof can be found.
reviewed by: Štefan Porubský
Mathematics Subject Classification ID: 11P99
Mathematics Subject Classification ID: 11-02
Mathematics Subject Classification ID: 11B13
Mathematics Subject Classification ID: 11P05
Mathematics Subject Classification ID: 11B05
zbMATH DE Number: 6485538
zbMATH Keywords: additive basis
zbMATH Keywords: asymptotic additive basis
zbMATH Keywords: thin additive basis
zbMATH Keywords: densities
zbMATH Keywords: Schnirelmann inequality
zbMATH Keywords: Mann inequality
zbMATH Keywords: van der Waerden, Szemerédi and Green-Tao theorems
zbMATH Keywords: Pollock conjectures
zbMATH Keywords: van der Waerden number
MaRDI profile type: Publication
full work available at URL: s40863-015-0006-4
OpenAlex ID: W2132357343
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Wikidata QID: Q121620685
DOI: 10.1007/S40863-015-0006-4
description: scientific article; zbMATH DE number 6485538