On Sumsets and Spectral Gaps
| dc.creator | Croot, Ernie | |
| dc.creator | Schoen, Tomasz | |
| dc.date | 2007-08-02 | |
| dc.date | 2007-11-28 | |
| dc.date.accessioned | 2026-07-07T08:45:12Z | |
| dc.date.available | 2026-07-07T08:45:12Z | |
| dc.description | It is well known that if S is a subset of the integers mod p, and if the second-largest Fourier coefficient is ``small'' relative to the largest coefficient, then the sumset S+S is much larger than S. We show in the present paper that if instead of having such a large ``spectral gap'' between the largest and second-largest Fourier coefficients, we had it between the kth largest and the (k+1)st largest, the same thing holds true, namely that |S+S| is appreciably larger than |S|. Well, we only do this for k < (log p)/(log 4). We also obtain analogous results for repeated sumsets S+S+...+S, and it turns out that the more terms one includes, the larger the index k that can be used. | |
| dc.description | A few typos have been corrected. Also theorem 2 in the last draft should have said ``t >= 3'', not ``t >= 2'' | |
| dc.identifier | https://arxiv.org/abs/0708.0381 | |
| dc.identifier | http://arxiv.org/abs/0708.0381 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142897 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05D99 | |
| dc.title | On Sumsets and Spectral Gaps | |
| dc.type | text |