On the Decay of the Fourier Transform and Three Term Arithmetic Progressions
| dc.creator | Croot, Ernie | |
| dc.date | 2006-07-07 | |
| dc.date | 2006-09-15 | |
| dc.date.accessioned | 2026-07-07T07:18:10Z | |
| dc.date.available | 2026-07-07T07:18:10Z | |
| dc.description | In this paper we prove a basic theorem which says that if f : F_p^n -> [0,1] has the property that ||f^||_(1/3) is not too ``large''(actually, it also holds for quasinorms 1/2-δin place of 1/3), and E(f) = p^{-n} sum_m f(m) is not too ``small'', then there are lots of triples m,m+d,m+2d such that f(m)f(m+d)f(m+2d) > 0. If f is the indicator function for some set S, then this would be saying that the set has many three-term arithmetic progressions. In principle this theorem can be applied to sets having very low density, where |S| is around p^{n(1-c)} for some small c > 0. | |
| dc.description | One small notational correction: In the paper I called ||f||_(1/3) a `norm', when in fact it should be 'quasinorm'. This does not affect any results, as I don't use the triangle inequality anywhere -- the 1/3 quasinorm was only used as a convenient way to state a corollary of one of my results | |
| dc.identifier | https://arxiv.org/abs/math/0607209 | |
| dc.identifier | http://arxiv.org/abs/math/0607209 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114204 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11P70 | |
| dc.title | On the Decay of the Fourier Transform and Three Term Arithmetic Progressions | |
| dc.type | text |