Last updated
2022-11-05T12:41:04.48+00:00
Abstract
Let F be a fixed finite field of characteristic at least 5. Let G = F^n be
the n-dimensional vector space over F, and write N := |G|. We show that if A is
a subset of G with size at least c_F N(log N)^{-c}, for some absolute constant
c > 0 and some c_F > 0, then A contains four distinct elements in arithmetic
progression.
This is equivalent, in the usual notation of additive combinatorics, to the
assertion that r_4(G) <<_F N(log N)^{-c}.
the n-dimensional vector space over F, and write N := |G|. We show that if A is
a subset of G with size at least c_F N(log N)^{-c}, for some absolute constant
c > 0 and some c_F > 0, then A contains four distinct elements in arithmetic
progression.
This is equivalent, in the usual notation of additive combinatorics, to the
assertion that r_4(G) <<_F N(log N)^{-c}.
Symplectic ID
398484
Download URL
http://arxiv.org/abs/math/0509560v3
Submitted to ORA
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Publication type
Journal Article
Publication date
23 Sep 2005