A Generalization of Roth's Theorem in Function Fields
| dc.contributor.author | Liu, Yu-Ru | |
| dc.contributor.author | Zhao, Xiaomei | |
| dc.date.accessioned | 2023-10-03T14:54:41Z | |
| dc.date.available | 2023-10-03T14:54:41Z | |
| dc.date.issued | 2012-11 | |
| dc.description | Copyright © 2012 The University of Michigan | en |
| dc.description.abstract | For n ∈ N = {1, 2, ...}, let D3([1, n]) denote the maximal cardinality of an integer subset of [1, n] containing no nontrivial 3-term arithmetic progression. In a fundamental paper [9], Roth proved that D3([1, n]) n/log log n. His result was later improved by Heath-Brown [4] and Szemerédi [11] to D3([1, n]) n/(log n)α for some small positive constant α > 0 (α = 1/20 in [11]). By introducing the notion of Bohr sets, Bourgain [2; 3] further improved this bound and showed that D3([1, n]) n(log log n)2 /(log n)2/3 | en |
| dc.description.sponsorship | Research partially supported by an NSERC Discovery Grant. | en |
| dc.identifier.uri | https://doi.org/10.1307/mmj/1353098515 | |
| dc.identifier.uri | http://hdl.handle.net/10012/19987 | |
| dc.language.iso | en | en |
| dc.publisher | University of Michigan, Department of Mathematics | en |
| dc.relation.ispartofseries | Michigan Math Journal;61(4) | |
| dc.title | A Generalization of Roth's Theorem in Function Fields | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Liu, Y.-R., & Zhao, X. (2012). A generalization of Roth’s theorem in function fields. Michigan Mathematical Journal, 61(4). https://doi.org/10.1307/mmj/1353098515 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Pure Mathematics | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |