Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in
  finite field geometries revisited   Let p > 4 be a prime. We show that the largest subset of F_p^n with no 4-term
arithmetic progressions has cardinality << N(log N)^{-c}, where c = 2^{-22} and
N := p^n. A result of this type was claimed in a previous paper by the authors
and published in Proc. London Math. Society. Unfortunately the proof had a gap,
and we issue an erratum for that paper here. Our new argument is different and
significantly shorter. In fact we prove a stronger result, which can be viewed
as a quantatitive version of some previous results of Bergelson-Host-Kra and
the authors.

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The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex