Rational points on X_0^+ (p^r)
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BILU, Yu. | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PARENT, Pierre | |
| hal.structure.identifier | Laboratoire de Mathématiques Blaise Pascal [LMBP] | |
| dc.contributor.author | REBOLLEDO, M. | |
| dc.date.accessioned | 2024-04-04T02:23:19Z | |
| dc.date.available | 2024-04-04T02:23:19Z | |
| dc.date.created | 2011-04-24 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189727 | |
| dc.description.abstractEn | We show how the recent isogeny bounds due to É. Gaudron and G. Rémond allow to obtain the triviality of X_0^+ (p^r)(Q), for r>1 and p a prime exceeding 2.10^{11}. This includes the case of the curves X_split (p). We then prove, with the help of computer calculations, that the same holds true for p in the range 10 < p < 10^{14}, p\neq 13. The combination of those results completes the qualitative study of such sets of rational points undertook in previous papers, with the exception of p=13. | |
| dc.language.iso | en | |
| dc.subject.en | Elliptic curves | |
| dc.subject.en | Serre's uniformity problem | |
| dc.title.en | Rational points on X_0^+ (p^r) | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1104.4641 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00772014 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00772014v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BILU,%20Yu.&PARENT,%20Pierre&REBOLLEDO,%20M.&rft.genre=preprint |
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