Real Analysis Exchange

Erdős Semi-groups, Arithmetic Progressions, and Szemerédi’s Theorem

Han Yu

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Abstract

In this paper, we introduce and study a certain type of sub-semigroup of \(\mathbb{R}/\mathbb{Z}\) which turns out to be closely related to Szemerédi’s theorem on arithmetic progressions.

Article information

Source
Real Anal. Exchange, Volume 44, Number 1 (2019), 101-118.

Dates
First available in Project Euclid: 27 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.rae/1561622435

Digital Object Identifier
doi:10.14321/realanalexch.44.1.0101

Mathematical Reviews number (MathSciNet)
MR3951337

Zentralblatt MATH identifier
07088966

Subjects
Primary: 26A03: Foundations: limits and generalizations, elementary topology of the line 37A45: Relations with number theory and harmonic analysis [See also 11Kxx]
Secondary: 28A80: Fractals [See also 37Fxx]

Keywords
Hausdorff dimension sum sets Szemeredi theorem

Citation

Yu, Han. Erdős Semi-groups, Arithmetic Progressions, and Szemerédi’s Theorem. Real Anal. Exchange 44 (2019), no. 1, 101--118. doi:10.14321/realanalexch.44.1.0101. https://projecteuclid.org/euclid.rae/1561622435


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