A Prime Analogue of Roth's Theorem in Function Fields
| dc.contributor.author | Liu, Yu-Ru | |
| dc.contributor.author | Spencer, Craig V. | |
| dc.date.accessioned | 2023-10-03T15:13:52Z | |
| dc.date.available | 2023-10-03T15:13:52Z | |
| dc.date.issued | 2015 | |
| dc.description.abstract | Abstract. Let Fq[t] denote the polynomial ring over the nite eld Fq, and let PR denote the subset of Fq[t] containing all monic irreducible polynomials of degree R. For non-zero elements r = (r1; r2; r3) of Fq satisfying r1 + r2 + r3 = 0, let D(PR) = Dr(PR) denote the maximal cardinality of a set AR PR which contains no non-trivial solution of r1x1 + r2x2 + r3x3 = 0 with xi 2 AR (1 i 3). By applying the polynomial Hardy-Littlewood circle method, we prove that D(PR) q jPRj=(log log log log jPRj). | en |
| dc.description.sponsorship | NSERC Discovery Grant || NSA Young Investigator Grant, #H98230-10-1-0155, #H98230-12-1-0220, #H98230-14-1-0164. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/20004 | |
| dc.language.iso | en | en |
| dc.publisher | Springer New York | en |
| dc.relation.ispartofseries | Advances in the Theory of Numbers; | |
| dc.subject | Roth's theorem | en |
| dc.subject | function fields | en |
| dc.subject | circle method | en |
| dc.subject | irreducible polynomials | en |
| dc.title | A Prime Analogue of Roth's Theorem in Function Fields | en |
| dc.type | Book Chapter | en |
| dcterms.bibliographicCitation | Liu, Y.-R. & Spencer, C.V. (2015). A Prime Analogue of Roth's Theorem in Function Fields. In A. Alaca; S. Alaca & K.S. Williams (Eds.), Advances in the Theory of Numbers: Proceedings of the Thirteenth Conference of the Canadian Number Theory Association. Springer New York. | 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 |