تقرير
Tamagawa number conjecture for CM modular forms and Rankin--Selberg convolutions
| العنوان: | Tamagawa number conjecture for CM modular forms and Rankin--Selberg convolutions |
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| المؤلفون: | Castella, Francesc |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | Let $E/F$ be an elliptic curve defined over a number field $F$ with complex multiplication by an imaginary quadratic field $K$ such that $F(E_{\rm tors})/K$ is abelian. In this paper we prove the $p$-part of the Birch and Swinnerton-Dyer formula for $E/F$ in analytic rank $1$ for primes $p>3$ split in $K$. This was previously known for $F=\mathbb{Q}$ by work of Rubin by a different method. We also prove a similar result for CM abelian varieties $A/K$, and for CM modular forms of higher weight. Comment: 36 pages. Comments very welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.11891 |
| رقم الأكسشن: | edsarx.2407.11891 |
| قاعدة البيانات: | arXiv |
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