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. Societ...
| Päätekijät: | , |
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| Aineistotyyppi: | Journal article |
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2012
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| _version_ | 1826297768185954304 |
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| author | Green, B Tao, T |
| author_facet | Green, B Tao, T |
| author_sort | Green, B |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:36:41Z |
| format | Journal article |
| id | oxford-uuid:d02acdb6-c98b-4ab7-a85a-035d59f4330a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:36:41Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:d02acdb6-c98b-4ab7-a85a-035d59f4330a2022-03-27T07:48:08ZNew bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisitedJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d02acdb6-c98b-4ab7-a85a-035d59f4330aSymplectic Elements at Oxford2012Green, BTao, TLet 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. |
| spellingShingle | Green, B Tao, T New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited |
| title | New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in
finite field geometries revisited |
| title_full | New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in
finite field geometries revisited |
| title_fullStr | New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in
finite field geometries revisited |
| title_full_unstemmed | New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in
finite field geometries revisited |
| title_short | New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in
finite field geometries revisited |
| title_sort | new bounds for szemeredi s theorem ia progressions of length 4 in finite field geometries revisited |
| work_keys_str_mv | AT greenb newboundsforszemeredistheoremiaprogressionsoflength4infinitefieldgeometriesrevisited AT taot newboundsforszemeredistheoremiaprogressionsoflength4infinitefieldgeometriesrevisited |