Long arithmetic progressions in critical sets

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:113

Article

Croot, E

关键词: arithmetic progressions;    additive number theory;    number theory;    arithmetic combinatorics;    additive combinatorics;    three-term arithmetic progressions;   

DOI  :  10.1016/j.jcta.2005.02.008

来源: Elsevier

【 摘 要 】

Given a density 0 < sigma <= 1, we show for all sufficiently large primes p that if S subset of Z/pZ has the least number of three-term arithmetic progressions among all sets with at least up elements, then S contains an arithmetic progression of length at least log(1/4+o(1))p. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free