A new proof of Roth's theorem on arithmetic progressions
| dc.creator | Croot, Ernie | |
| dc.creator | Sisask, Olof | |
| dc.date | 2008-01-16 | |
| dc.date | 2008-04-01 | |
| dc.date.accessioned | 2026-07-07T09:29:16Z | |
| dc.date.available | 2026-07-07T09:29:16Z | |
| dc.description | 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. | |
| dc.description | 6 pages. To appear in Proceedings of the AMS | |
| dc.identifier | https://arxiv.org/abs/0801.2577 | |
| dc.identifier | http://arxiv.org/abs/0801.2577 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157724 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05D99 | |
| dc.title | A new proof of Roth's theorem on arithmetic progressions | |
| dc.type | text |