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Rational points on X_0^+ (p^r)

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBILU, Yu.
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPARENT, Pierre
hal.structure.identifierLaboratoire de Mathématiques Blaise Pascal [LMBP]
dc.contributor.authorREBOLLEDO, M.
dc.date.accessioned2024-04-04T02:23:19Z
dc.date.available2024-04-04T02:23:19Z
dc.date.created2011-04-24
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189727
dc.description.abstractEnWe 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.isoen
dc.subject.enElliptic curves
dc.subject.enSerre's uniformity problem
dc.title.enRational points on X_0^+ (p^r)
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv1104.4641
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00772014
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00772014v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.au=BILU,%20Yu.&amp;PARENT,%20Pierre&amp;REBOLLEDO,%20M.&amp;rft.genre=preprint


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