Journal of East China Normal University(Natural Sc ›› 2007, Vol. 2007 ›› Issue (5): 12-19.

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Criterion for Elliptic Curves with the Lowest 3-Power in L(1)(Chinese)

SUN Nai-zhe   

  1. Department of Mathematics, Tianjin University of Science and Technology, Tianjin 300457, China
  • Received:2006-11-01 Revised:2007-02-26 Online:2007-09-25 Published:2007-09-25
  • Contact: SUN Nai-zhe

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Abstract: Let K be the 3rd cyclotomic field, E D[lambda] :y2=x3-24 3 3 D[lambda]] be an elliptic curve defined over K, where D\in K is a square-free algebraic integer and [[lambda]] in Z . Qiu Derong found a rather complicated function as the criterion for the value of the Hecke L-function attached to the curve E D[lambda]([lambda]=2,4) at s=1 divided by the period [OMEGA] to be exactly divisible by 3 n/2 -1 . This paper reduced Qiu’s criterion to a simpler version in terms of weighted graphs.

Key words: complex multiplication, Hecke L-function, weighted graph, spanning tree, elliptic curves, complex multiplication, Hecke L-function, weighted graph, spanning tree

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