New bounds for Szemeredi's Theorem, I: Progressions of length 4 in finite field geometries
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 distinc...
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| Format: | Journal article |
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2005
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| _version_ | 1826260379258322944 |
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| author | Green, B Tao, T |
| author_facet | Green, B Tao, T |
| author_sort | Green, B |
| collection | OXFORD |
| description | 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}. |
| first_indexed | 2024-03-06T19:04:42Z |
| format | Journal article |
| id | oxford-uuid:14bc8023-cf8b-4491-81d2-761d6ac3543b |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:04:42Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | oxford-uuid:14bc8023-cf8b-4491-81d2-761d6ac3543b2022-03-26T10:21:25ZNew bounds for Szemeredi's Theorem, I: Progressions of length 4 in finite field geometriesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:14bc8023-cf8b-4491-81d2-761d6ac3543bSymplectic Elements at Oxford2005Green, BTao, TLet 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}. |
| spellingShingle | Green, B Tao, T New bounds for Szemeredi's Theorem, I: Progressions of length 4 in finite field geometries |
| title | New bounds for Szemeredi's Theorem, I: Progressions of length 4 in
finite field geometries |
| title_full | New bounds for Szemeredi's Theorem, I: Progressions of length 4 in
finite field geometries |
| title_fullStr | New bounds for Szemeredi's Theorem, I: Progressions of length 4 in
finite field geometries |
| title_full_unstemmed | New bounds for Szemeredi's Theorem, I: Progressions of length 4 in
finite field geometries |
| title_short | New bounds for Szemeredi's Theorem, I: Progressions of length 4 in
finite field geometries |
| title_sort | new bounds for szemeredi s theorem i progressions of length 4 in finite field geometries |
| work_keys_str_mv | AT greenb newboundsforszemeredistheoremiprogressionsoflength4infinitefieldgeometries AT taot newboundsforszemeredistheoremiprogressionsoflength4infinitefieldgeometries |