On certain other sets of integers

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Tom Sanders This is my paper · ORCID

classification math.NTmath.CA

keywords arithmeticcertaincontainingintegersnon-trivialotherprogressionssets

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We show that if A is a subset of {1,...,N} containing no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{3/4-o(1)} N).

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On Fourier coefficients of sets with small doubling
math.CO 2024-12 conditional novelty 7.0 of 10

Under the condition 100K^2 δ ≤ 1, a set with small doubling and small Fourier coefficients must have a dense intersection with a translate of a large regular Bohr set of controlled dimension.