论文标题
Mahler的度量和椭圆曲线具有潜在的复杂乘法
Mahler's measure and elliptic curves with potential complex multiplication
论文作者
论文摘要
给定在$ \ mathbb {q} $上定义的椭圆曲线$ e $，该$具有潜在的复杂乘法，由整数$ \ mathcal {o} _k $ \ mathcal {o} _k $的假想二次field $ k $我们构建一个pynomial $ p_e \ in \ nathbb {z} $ e $ e $ $ m（p_e）\ in \ mathbb {r} $与$ l $ -function $ l（e，s）$ at $ s = 2 $的特殊值有关。
Given an elliptic curve $E$ defined over $\mathbb{Q}$ which has potential complex multiplication by the ring of integers $\mathcal{O}_K$ of an imaginary quadratic field $K$ we construct a polynomial $P_E \in \mathbb{Z}[x,y]$ which is a planar model of $E$ and such that the Mahler measure $m(P_E) \in \mathbb{R}$ is related to the special value of the $L$-function $L(E,s)$ at $s = 2$.
