中国科学院研究生院学报2012，Vol.29Issue(2)：154-161,8.
关于费玛曲线xN+yN=1的K2群的一些注记
Some remarks on K2 of Fermat curve xN + yN =1
摘要
Abstract
We first review Beilinson's conjecture for a smooth projective curve C over Q.Then we exhibit an element in K2-group of the Fermat curve XN:xN + yN =1 from a toric variety viewpoint.Finally,we focus on the special case of X3 and explicitly express its Hasse-Weil L-function L( X3,s)in terms of the Eisenstein-Kronecker-Lerch series,which allows us to verify that L(X3,s) satisfies a certain functional equation and has a meromorphic continuation in the entire complex plane.关键词
Beilinson猜想/K2群/费玛曲线/椭圆簇/CM椭圆曲线/L-函数/Eisenstein-Kronecker-Lerch级数Key words
Beilinson's conjecture/K2-group/Fermat curve/toric variety/CM elliptic curve/Hasse-Weil L-function/Eisenstein-Kronecker-Lerch series分类
数理科学引用本文复制引用
田博,唐国平,陈虹..关于费玛曲线xN+yN=1的K2群的一些注记[J].中国科学院研究生院学报,2012,29(2):154-161,8.基金项目
Supported by National NSFC (11071247) （11071247）
