dc.contributor.author | Kuo, Wentang | |
dc.contributor.author | Liu, Yu-Ru | |
dc.date.accessioned | 2023-10-03 15:09:35 (GMT) | |
dc.date.available | 2023-10-03 15:09:35 (GMT) | |
dc.date.issued | 2009-12 | |
dc.identifier.uri | https://doi.org/10.1112/jlms/jdp043 | |
dc.identifier.uri | http://hdl.handle.net/10012/19997 | |
dc.description | This is the peer reviewed version of the following article: Kuo, W., & Liu, Y.-R. (2009b). Cyclicity of finite Drinfeld modules. Journal of the London Mathematical Society, 80(3), 567–584, which has been published in final form at https://doi.org/10.1112/jlms/jdp043. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. | en |
dc.description.abstract | Le tA=Fq[T] be the polynomial ring over the finite field Fq,letk=Fq(T) be the rational function field, and let K be a finite extension of k. For a prime P of K, we denote by OP the valuation ring of P, by MP the maximal ideal of OP, and by FP the residue field OP/MP. Let φ be a DrinfeldA-module over K of rankr. If φ has good reduction at P, let φ ⊗ FP denote the reduction of φ at P and letφ(FP) denote the A-module (φ⊗FP)(FP). Ifφis of rank 2 with End ̄K(φ)=A, then we obtain an asymptotic formula for the number of primes P of K of degree x for which φ (FP) is cyclic. This result can be viewed as a Drinfeld module analogue of Serre’s cyclicity result on elliptic curves. We also show that whenφis of rankr 3 a similar result follows. | en |
dc.description.sponsorship | This research was supported by an NSERC Discovery Grant. | en |
dc.language.iso | en | en |
dc.publisher | Wiley | en |
dc.relation.ispartofseries | Journal of the London Mathematical Society;80(3) | |
dc.title | Cyclicity of finite Drinfeld modules | en |
dc.type | Article | en |
dcterms.bibliographicCitation | Kuo, W., & Liu, Y.-R. (2009b). Cyclicity of finite Drinfeld modules. Journal of the London Mathematical Society, 80(3), 567–584. https://doi.org/10.1112/jlms/jdp043 | en |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.contributor.affiliation2 | Pure Mathematics | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Reviewed | en |
uws.scholarLevel | Faculty | en |