p-adic heights of Heegner points and Λ-adic regulators
p-adic heights of Heegner points and Λ-adic regulators
复制标题
Heegner 点的 p 进高度和 Λ 进调节器
DOI：
10.1090/s0025-5718-2014-02876-7
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
W. Stein
中科院分区：
文献类型：
--
作者：
Jennifer S. Balakrishnan;M. Çiperiani;W. Stein
设E是定义在q上的一条椭圆曲线，本文的目的是使计算Mazur-Rubin和Howard研究过的E的Heegner l -函数和抗细胞组织Λ-adic调节因子成为可能。我们推广了Cohen和Watkins的结果，从而计算了非基本判别的Heegner点。然后证明了在数域上定义的E点的分母与其x坐标的最小多项式的前导系数之间的关系。利用这种关系，我们改写了Mazur， Stein和Tate早期的工作，以产生有效的算法来计算在数域上定义的E点的p进高度。这些方法使我们能够给出Heegner l -函数和抗细胞分裂Λ-adic调节因子的第一个明确的例子。
Let E be an elliptic curve defined over Q. The aim of this paper is to make it possible to compute Heegner L-functions and anticyclotomic Λ-adic regulators of E, which were studied by Mazur-Rubin and Howard. We generalize results of Cohen and Watkins and thereby compute Heegner points of nonfundamental discriminant. We then prove a relationship between the denominator of a point of E defined over a number field and the leading coefficient of the minimal polynomial of its xcoordinate. Using this relationship, we recast earlier work of Mazur, Stein, and Tate to produce effective algorithms to compute p-adic heights of points of E defined over number fields. These methods enable us to give the first explicit examples of Heegner L-functions and anticyclotomic Λ-adic regulators.
椭圆曲线上的 3-adic 高度
影响因子：
0.7
作者：
Balakrishnan J
通讯作者：
Balakrishnan J