On large subsets of F nq with no three-termarithmetic progression

By Jordan S. Ellenberg, D. Gijswijt. 2017

256 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions. (2020, unknown): “Indeed, when studying three-term arithmetic progressions in F3 the polynomial method is both much simpler and gives far superior quantitative bounds (namely an upper bound of |A| 6 c for some c < 3), as shown by Ellenberg and Gijswijt [12].”
The lean mathematical library (2019, background): “Their celebrated proof [23], published in the Annals of Mathematics in 2017, was noted for its use of elementary methods from linear algebra.”
Mathematical discoveries from program search with large language models (2023, background): “For instance, progress towards improved upper bounds for the cap set problem 30,31 immediately led to a series of other combinatorial results, for example, on the Erdös–Radio sunflower problem 32 .”