Roth's theorem in the primes
We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain wh...
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| Format: | Journal article |
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2003
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| _version_ | 1826278441168666624 |
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| author | Green, B |
| author_facet | Green, B |
| author_sort | Green, B |
| collection | OXFORD |
| description | We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes. |
| first_indexed | 2024-03-06T23:43:57Z |
| format | Journal article |
| id | oxford-uuid:70441a56-b6d5-493b-8f7b-88811d86dea3 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:43:57Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:70441a56-b6d5-493b-8f7b-88811d86dea32022-03-26T19:36:00ZRoth's theorem in the primesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:70441a56-b6d5-493b-8f7b-88811d86dea3Symplectic Elements at Oxford2003Green, BWe show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes. |
| spellingShingle | Green, B Roth's theorem in the primes |
| title | Roth's theorem in the primes |
| title_full | Roth's theorem in the primes |
| title_fullStr | Roth's theorem in the primes |
| title_full_unstemmed | Roth's theorem in the primes |
| title_short | Roth's theorem in the primes |
| title_sort | roth s theorem in the primes |
| work_keys_str_mv | AT greenb rothstheoremintheprimes |