Rational points on X_0^+ (p^r)
| Autor: | Bilu, Yu., Parent, P., Rebolledo, M. |
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| Rok vydání: | 2011 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show how the recent isogeny bounds due to \'E. Gaudron and G. R\'emond 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. Comment: 16 pages, no figure |
| Databáze: | arXiv |
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