论文标题
椭圆曲线的扭曲L值的完整性
Integrality of twisted L-values of elliptic curves
论文作者
论文摘要
在椭圆曲线上的合适的，相当弱的假设下，$ e/\ mathbb {q} $和原始的非客气的dirichlet字符$花例如，对于半曲线，$ \ mathscr {l}（e，χ）$都是不可或缺的，只要$ e $允许在$ \ m athbb {q} $上定义的iSogenies。此外，我们举例说明了我们的假设对于构成的必要性是必要的。
Under suitable, fairly weak hypotheses on an elliptic curve $E/\mathbb{Q}$ and a primitive non-trivial Dirichlet character $χ$, we show that the algebraic $L$-value $\mathscr{L}(E,χ)$ at $s=1$ is an algebraic integer. For instance, for semistable curves $\mathscr{L}(E,χ)$ is integral whenever $E$ admits no isogenies defined over $\mathbb{Q}$. Moreover we give examples illustrating that our hypotheses are necessary for integrality to hold.
