Sum-product phenomena in F_p: a brief introduction
These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 2009. The aim was to understand the simplest proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over subgroups. As a byproduct one obtains a clean proof of the Bourgain-Katz-Tao theore...
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| Materyal Türü: | Journal article |
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2009
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| _version_ | 1826300255035981824 |
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| author | Green, B |
| author_facet | Green, B |
| author_sort | Green, B |
| collection | OXFORD |
| description | These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 2009. The aim was to understand the simplest proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over subgroups. As a byproduct one obtains a clean proof of the Bourgain-Katz-Tao theorem on the sum-product phenomenon in F_p. The arguments are essentially extracted from a paper of Bourgain, and I benefitted very much from being in receipt of unpublished course notes of Elon Lindenstrauss. No originality is claimed. |
| first_indexed | 2024-03-07T05:14:23Z |
| format | Journal article |
| id | oxford-uuid:dcab92f5-4bc0-4485-a17f-c3f2e48b8ffa |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:14:23Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:dcab92f5-4bc0-4485-a17f-c3f2e48b8ffa2022-03-27T09:19:17ZSum-product phenomena in F_p: a brief introductionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dcab92f5-4bc0-4485-a17f-c3f2e48b8ffaSymplectic Elements at Oxford2009Green, BThese notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 2009. The aim was to understand the simplest proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over subgroups. As a byproduct one obtains a clean proof of the Bourgain-Katz-Tao theorem on the sum-product phenomenon in F_p. The arguments are essentially extracted from a paper of Bourgain, and I benefitted very much from being in receipt of unpublished course notes of Elon Lindenstrauss. No originality is claimed. |
| spellingShingle | Green, B Sum-product phenomena in F_p: a brief introduction |
| title | Sum-product phenomena in F_p: a brief introduction |
| title_full | Sum-product phenomena in F_p: a brief introduction |
| title_fullStr | Sum-product phenomena in F_p: a brief introduction |
| title_full_unstemmed | Sum-product phenomena in F_p: a brief introduction |
| title_short | Sum-product phenomena in F_p: a brief introduction |
| title_sort | sum product phenomena in f p a brief introduction |
| work_keys_str_mv | AT greenb sumproductphenomenainfpabriefintroduction |