A new proof of Roth's theorem on arithmetic progressions

Details A new proof of Roth's theorem on arithmetic progressions A new proof of Roth's theorem on arithmetic progressions

2008-01-16

arxiv.org/abs/0801.2577v2

Mathematics

Combinatorics

6 pages. To appear in Proceedings of the AMS

Scientific paper

We present a proof of Roth's theorem that follows a slightly different structure to the usual proofs, in that there is not much iteration. Although our proof works using a type of density increment argument (which is typical of most proofs of Roth's theorem), we do not pass to a progression related to the large Fourier coefficients of our set (as most other proofs of Roth do). Furthermore, in our proof, the density increment is achieved through an application of a quantitative version of Varnavides's theorem, which is perhaps unexpected.

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