论文标题
在Eisenstein Case中，将泰特 - 萨法尔维奇与伯诺利 - 赫维兹的数字连接到伯努利 - 赫维兹的数字的一致性关系
Congruence Relations Connecting Tate-Shafarevich Groups with Bernoulli-Hurwitz Numbers by Elliptic Gauss Sums in Eisenstein Case
论文作者
论文摘要
假想二次字段的类数量与伯努利号码或欧拉数字之间存在经典的一致性。在BSD猜想下，Onishi获得了这些一致性的椭圆概括，这在某些椭圆曲线的Tate-Shafarevich组的顺序与Ghuss Integers Ring和Mordell-Weil Rank 0的CM和CM之间提供了一致性，以及Mordell-Weil Rank 0，以及与椭圆函数相关功能与Gauss Integegegs Integeger egegers Remer Reneger的电源序列扩展的系数。在本文中，我们为Eisenstein Integers案提供了Onishi的类型一致性。
There are classical congruences between the class number of an imaginary quadratic field and a Bernoulli number or an Euler number. Under the BSD conjecture, Onishi obtained an elliptic generalization of these congruences, which gives congruences between the order of the Tate-Shafarevich group of certain elliptic curves with CM by the Gauss integers ring and Mordell-Weil rank 0, and a coefficient of power series expansion of an elliptic function associated to Gauss integers ring. In this paper, we provide Onishi's type congruences for the Eisenstein integers case.
