Data di Pubblicazione:
2018
Citazione:
Ramsey properties of nonlinear Diophantine equations / M. Di Nasso, L. Luperi Baglini. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 324(2018), pp. 84-117. [10.1016/j.aim.2017.11.003]
Abstract:
We present general sufficient and necessary conditions for the partition regularity of Diophantine equations, which extend the classic Rado’s Theorem by covering large classes of nonlin-ear equations. The goal is to contribute to an overall theory of Ramsey properties of (nonlinear) Diophantine equations that encompasses the known results in this area under a unified framework.
Sufficient conditions are obtained by exploiting algebraic properties in the space of ultrafilters βN, grounding on combi-natorial properties of positive density sets and IP sets. Neces-sary conditions are proved by a new technique in nonstandard analysis, based on the use of the relation of u-equivalence for the hypernatural numbers ∗N.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Ramsey Theory; Diophantine equations; Ultrafilters; Nonstandard analysis
Elenco autori:
M. Di Nasso, L. Luperi Baglini
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