A compendium of results in additive number theory
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.
van der Waerden, Szemerédi and Green-Tao theorems
scientific article; zbMATH DE number 6485538
scientific article