Subsets of F_p^n without three term arithmetic progressions have several large Fourier coefficients
| dc.creator | Croot, Ernie | |
| dc.date | 2007-07-10 | |
| dc.date.accessioned | 2026-07-07T08:14:54Z | |
| dc.date.available | 2026-07-07T08:14:54Z | |
| dc.description | Suppose that f : F_p^n -> [0,1] has expected value t in [p^(-n/9),1] (so, the density t can be quite low!). Furthermore, suppose that support(f) has no three-term arithmetic progressions. Then, we develop non-trivial lower bounds for f_j, which is the jth largest Fourier coefficient of f. This result is similar in spirit to that appearing in an earlier paper [1] by the author; however, in that paper the focus was on the ``small'' Fourier coefficients, whereas here the focus is on the ``large'' Fourier coefficients. Furthermore, the proof in the present paper requires much more sophisticated arguments than those of that other paper. | |
| dc.description | This is a preliminary draft. Later drafts will have more references and cleaner proofs | |
| dc.identifier | https://arxiv.org/abs/0707.1496 | |
| dc.identifier | http://arxiv.org/abs/0707.1496 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133296 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05D99 | |
| dc.title | Subsets of F_p^n without three term arithmetic progressions have several large Fourier coefficients | |
| dc.type | text |