On sets of polynomials whose difference set contains no squares
| dc.contributor.author | Hoang Le, Thai | |
| dc.contributor.author | Liu, Yu-Ru | |
| dc.date.accessioned | 2023-10-03T15:12:39Z | |
| dc.date.available | 2023-10-03T15:12:39Z | |
| dc.date.issued | 2013 | |
| dc.description.abstract | Let Fq[t] be the polynomial ring over the finite field Fq, and let GN be the subset of Fq[t] containing all polynomials of degree strictly less than N. Define D(N) to be the maximal cardinality of a set A⊆GN for which A−A contains no squares of polynomials. By combining the polynomial Hardy–Littlewood circle method with the density increment technology developed by Pintz, Steiger and Szemerédi, we prove that D(N)≪qN(logN)7/N. | en |
| dc.identifier.uri | https://doi.org/10.4064/aa161-2-2 | |
| dc.identifier.uri | http://hdl.handle.net/10012/20002 | |
| dc.language.iso | en | en |
| dc.publisher | Institute of Mathematics: Polish Academy of Sciences | en |
| dc.relation.ispartofseries | Acta Arithmetica;161 | |
| dc.subject | Sarkozy's theorem | en |
| dc.subject | function fields | en |
| dc.subject | circle method | en |
| dc.title | On sets of polynomials whose difference set contains no squares | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Lê, T. H., & Liu, Y.-R. (2013). On sets of polynomials whose difference set contains no squares. Acta Arithmetica, 161(2), 127–143. https://doi.org/10.4064/aa161-2-2 | 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 |