Journal of University of Chinese Academy of Sciences >
2012 >Issue 2: 154 - 161
Some remarks on K2 of Fermat curve xN+yN=1
Received date: 2011-03-28
Revised date: 2011-05-09
Online published: 2012-03-15
Supported by
Supported by National NSFC (11071247)
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.
TIAN Bo , TANG Guo-Ping , CHEN Hong . Some remarks on K2 of Fermat curve xN+yN=1[J]. Journal of University of Chinese Academy of Sciences, 2012 , (2) : 154 -161 . DOI: 10.7523/j.issn.2095-6134.2012.2.002
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