Density theorems for rational numbers
Andreas Koutsogiannis
TL;DR
This paper introduces rational measure-preserving systems and establishes conditions under which subsets of rational numbers contain arbitrarily long arithmetic progressions.
Contribution
It defines rational systems of measure-preserving transformations and proves a recurrence theorem that guarantees long arithmetic progressions in certain rational subsets.
Findings
Established a recurrence result for rational systems
Provided sufficient conditions for long arithmetic progressions
Extended classical recurrence theorems to rational number systems
Abstract
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic progressions.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Analytic Number Theory Research · Advanced Topology and Set Theory