The structure of critical sets for F_p arithmetic progressions
| dc.creator | Croot, Ernie | |
| dc.date | 2007-12-10 | |
| dc.date | 2008-02-19 | |
| dc.date.accessioned | 2026-07-07T09:21:22Z | |
| dc.date.available | 2026-07-07T09:21:22Z | |
| dc.description | Fix a prime p and a density 0 < d <= 1. Among all functions f : F_p -> [0,1], what can one say about those which assign minimal weight to three-term arithmetic progressions -- that is, the sum of f(a)f(a+x)f(a+2x) is minimal as we sum over all a and x -- subject to the density constraint that the expected value of f equals d? In the present paper we show three things about them: 1) Such f are nearly indicator functions; 2) They enjoy a certain ``local minimal'' property; and, 3) They are approximately indicator functions for certain sumsets A+B. | |
| dc.description | Light corrections, some more commentary in a few places. 20 pages | |
| dc.identifier | https://arxiv.org/abs/0712.1611 | |
| dc.identifier | http://arxiv.org/abs/0712.1611 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154997 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05D05 | |
| dc.title | The structure of critical sets for F_p arithmetic progressions | |
| dc.type | text |