CM椭圆曲线的$p$-adic Eisenstein-Kronecker级数与Kronecker极限公式
数论
2020-09-11 v2
摘要
考虑一条定义在虚二次域上的椭圆曲线，它在的素理想处具有好约化，并且由的完整整数环进行复乘法。本文中，我们为该椭圆曲线构造了Eisenstein-Kronecker级数的-adic类似物，作为椭圆曲线上的Coleman函数。随后，我们利用Kronecker theta函数的分布关系，证明了第一和第二Kronecker极限公式的-adic类似物。
引用
@article{arxiv.0807.4007,
title = {$p$-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas},
author = {Kenichi Bannai and Hidekazu Furusho and Shinichi Kobayashi},
journal= {arXiv preprint arXiv:0807.4007},
year = {2020}
}
备注
v2. The current version is the synthesis of {\S}1-{\S}3 of the first version of this article with the content of arXiv:0807.4008 "The Kronecker limit formulas via the distribution relation." {\S}4,{\S}5 of the first version of this paper will be treated in a subsequent article