تقرير
On the effective version of Serre's open image theorem
| العنوان: | On the effective version of Serre's open image theorem |
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| المؤلفون: | Mayle, Jacob, Wang, Tian |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11G05 (Primary) 11F80 (Secondary) |
| الوصف: | Let $E/\mathbb{Q}$ be an elliptic curve without complex multiplication. By Serre's open image theorem, the mod $\ell$ Galois representation $\overline{\rho}_{E, \ell}$ of $E$ is surjective for each prime number $\ell$ that is sufficiently large. Under the generalized Riemann hypothesis, we give an explicit upper bound on the largest prime $\ell$, linear in the logarithm of the conductor of $E$, such that $\overline{\rho}_{E, \ell}$ is nonsurjective. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1112/blms.13002 |
| URL الوصول: | http://arxiv.org/abs/2109.08656 |
| رقم الأكسشن: | edsarx.2109.08656 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1112/blms.13002 |
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