A quantitative improvement for Roth's theorem on arithmetic progressions: Table 1.
Year: 2016
Type: article
Abstract: 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 ( log log N ) 4 / log N . By the same method, we also improve the bounds in the analogous problem over F q [ t ] and for the problem of finding long arithmetic progressions in a sumset.
DOI: 10.1112/jlms/jdw010
Author: T. F. Bloom
Institution: University of Bristol
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2114487569