Waring's problem in function fields
| dc.contributor.author | Liu, Yu-Ru | |
| dc.contributor.author | Wooley, Trevor D. | |
| dc.date.accessioned | 2023-10-03T14:55:12Z | |
| dc.date.available | 2023-10-03T14:55:12Z | |
| dc.date.issued | 2010 | |
| dc.description | This article is published in the Journal fur die reine und angewandte Mathematik, https://doi.org/10.1515/crelle.2010.001 | en |
| dc.description.abstract | Let Fq½t denote the ring of polynomials over the finite field Fq of characteristic p, and write Jk q ½t for the additive closure of the set of kth powers of polynomials in Fq½t. Define GqðkÞ to be the least integer s satisfying the property that every polynomial in Jk q ½t of su‰ciently large degree admits a strict representation as a sum of s kth powers. We employ a version of the Hardy-Littlewood method involving the use of smooth polynomials in order to establish a bound of the shape GqðkÞeCk log k þ Oðk log log kÞ. Here, the coe‰cient C is equal to 1 when k < p, and C is given explicitly in terms of k and p when k > p, but in any case satisfies C e4=3. There are associated conclusions for the solubility of diagonal equations over Fq½t, and for exceptional set estimates in Waring’s problem. | en |
| dc.description.sponsorship | Research partially supported by an NSERC Discovery Grant || Research partially supported by NSF grant, DMS-0601367. | en |
| dc.identifier.uri | https://doi.org/10.1515/crelle.2010.001 | |
| dc.identifier.uri | http://hdl.handle.net/10012/19988 | |
| dc.language.iso | en | en |
| dc.publisher | De Gruyter | en |
| dc.relation.ispartofseries | Journal fur die reine und angewandte Mathematik;638 | |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.title | Waring's problem in function fields | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Liu, Y.-R., & Wooley, T. D. (2010). Waring’s problem in function fields. Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal), 2010(638), 1–67. https://doi.org/10.1515/crelle.2010.001 | 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 |