The Minimal Number of Three-Term Arithmetic Progressions Modulo a Prime Converges to a Limit
| dc.creator | Croot, Ernie | |
| dc.date | 2004-12-31 | |
| dc.date | 2006-07-07 | |
| dc.date.accessioned | 2026-07-07T06:39:14Z | |
| dc.date.available | 2026-07-07T06:39:14Z | |
| dc.description | Given a density t in (0,1], and a prime p, let S be any subset of F_p having at least tp elements, and having the least number of three-term arithmetic progressions mod p among all subsets of F_p with at least tp elements. Define N(t,p) to be 1/p^2 times the number of three-term arithmetic progressions in S modulo p. Note that N(t,p) does not depend on S -- it only depends on t and p. An old result of Varnavides shows that for fixed t, N(t,p) > c(t) > 0 for all primes p sufficiently large. But, does N(t,p) converge to a limit as p -> infinity? We prove that it does. | |
| dc.description | This draft is a significantly shorter proof of the theorem. To appear in Canadian Math Bulletin | |
| dc.identifier | https://arxiv.org/abs/math/0501004 | |
| dc.identifier | http://arxiv.org/abs/math/0501004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101002 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11P99 | |
| dc.title | The Minimal Number of Three-Term Arithmetic Progressions Modulo a Prime Converges to a Limit | |
| dc.type | text |