Title of article
Long arithmetic progressions in critical sets
Author/Authors
Croot، نويسنده , , Ernie، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2006
Pages
14
From page
53
To page
66
Abstract
Given a density 0 < σ ⩽ 1 , we show for all sufficiently large primes p that if S ⊆ Z / p Z has the least number of three-term arithmetic progressions among all sets with at least σ p elements, then S contains an arithmetic progression of length at least log 1 / 4 + o ( 1 ) p .
Keywords
arithmetic progressions , number theory , additive combinatorics , additive number theory , Three-term arithmetic progressions , Arithmetic combinatorics
Journal title
Journal of Combinatorial Theory Series A
Serial Year
2006
Journal title
Journal of Combinatorial Theory Series A
Record number
1531036
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