A quantitative improvement for Roth's theorem on arithmetic progressions

A quantitative improvement for Roth's theorem on arithmetic progressions

We improve the quantitative estimate for Roth's theorem on three-term arithmetic progressions, showing that if 𝐴⊂{1,...,𝑁} contains no non-trivial three-term arithmetic progressions, then |𝐴|≪𝑁(loglog𝑁)4/log𝑁 . By the same method, we also improve the bounds in the analogous problem over 𝔽𝑞[...

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Príomhchruthaitheoir: Bloom, TF
Formáid: Journal article
Teanga:English
Foilsithe / Cruthaithe: Wiley 2016
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Achoimre:We improve the quantitative estimate for Roth's theorem on three-term arithmetic progressions, showing that if 𝐴⊂{1,...,𝑁} contains no non-trivial three-term arithmetic progressions, then |𝐴|≪𝑁(loglog𝑁)4/log𝑁 . By the same method, we also improve the bounds in the analogous problem over 𝔽𝑞[𝑡] and for the problem of finding long arithmetic progressions in a sumset.

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