Logarithmic bounds for Roth’s theorem via almost-periodicity
We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if A⊂{1,2,…,N} is free of three-term progressions, then |A|≤N/(logN)1−o(1). Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity.
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Diamond Open Access Journals
2019
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| _version_ | 1826292656748101632 |
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| author | Bloom, TF Sisask, O |
| author_facet | Bloom, TF Sisask, O |
| author_sort | Bloom, TF |
| collection | OXFORD |
| description | We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if A⊂{1,2,…,N} is free of three-term progressions, then |A|≤N/(logN)1−o(1). Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity. |
| first_indexed | 2024-03-07T03:18:04Z |
| format | Journal article |
| id | oxford-uuid:b67ba979-021b-4b8d-bca2-9cc06f68bb91 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:18:04Z |
| publishDate | 2019 |
| publisher | Diamond Open Access Journals |
| record_format | dspace |
| spelling | oxford-uuid:b67ba979-021b-4b8d-bca2-9cc06f68bb912022-03-27T04:41:17ZLogarithmic bounds for Roth’s theorem via almost-periodicityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b67ba979-021b-4b8d-bca2-9cc06f68bb91EnglishSymplectic ElementsDiamond Open Access Journals2019Bloom, TFSisask, OWe give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if A⊂{1,2,…,N} is free of three-term progressions, then |A|≤N/(logN)1−o(1). Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity. |
| spellingShingle | Bloom, TF Sisask, O Logarithmic bounds for Roth’s theorem via almost-periodicity |
| title | Logarithmic bounds for Roth’s theorem via almost-periodicity |
| title_full | Logarithmic bounds for Roth’s theorem via almost-periodicity |
| title_fullStr | Logarithmic bounds for Roth’s theorem via almost-periodicity |
| title_full_unstemmed | Logarithmic bounds for Roth’s theorem via almost-periodicity |
| title_short | Logarithmic bounds for Roth’s theorem via almost-periodicity |
| title_sort | logarithmic bounds for roth s theorem via almost periodicity |
| work_keys_str_mv | AT bloomtf logarithmicboundsforrothstheoremviaalmostperiodicity AT sisasko logarithmicboundsforrothstheoremviaalmostperiodicity |