Near arithmetic progressions in sparse sets

DOI10.1090/S0002-9939-05-08141-4zbMath1090.11011MaRDI QIDQ3375409

Steven C. Leth

Publication date: 8 March 2006

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

nonstandard analysisarithmetic progressionscelldensity conditionsErdős-Túran conjecture

Mathematics Subject Classification ID

Density, gaps, topology (11B05) Nonstandard models of arithmetic (03H15) Arithmetic progressions (11B25) Nonstandard models in mathematics (03H05) Nonstandard arithmetic (number-theoretic aspects) (11U10)

Related Items (2)

Inverse problem for cuts ⋮ High density piecewise syndeticity of sumsets

Cites Work

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• Sequences in countable nonstandard models of the natural numbers
• Some nonstandard methods in combinatorial number theory
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Nonstandard methods for upper Banach density problems.
• The primes contain arbitrarily long arithmetic progressions
• The sumset phenomenon
• Inverse problem for upper asymptotic density
• Applications of Nonstandard Models and Lebesgue Measure to Sequences of Natural Numbers
• On sets of integers containing k elements in arithmetic progression
• Applications of Nonstandard Analysis in Additive Number Theory
• A new proof of Szemerédi's theorem

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