SplitCM points and central values of Hecke Lseries
Abstract
SplitCM points are points of the moduli space h_2/Sp_4(Z) corresponding to products $E \times E'$ of elliptic curves with the same complex multiplication. We prove that the number of splitCM points in a given class of h_2/Sp_4(Z) is related to the coefficients of a weight 3/2 modular form studied by Eichler. The main application of this result is a formula for the central value $L(\psi_N, 1)$ of a certain Hecke Lseries. The Hecke character $\psi_N$ is a twist of the canonical Hecke character $\psi$ for the elliptic Qcurve A studied by Gross, and formulas for $L(\psi, 1)$ as well as generalizations were proven by Villegas and Zagier. The formulas for $L(\psin, 1)$ are easily computable and numerical examples are given.
 Publication:

arXiv eprints
 Pub Date:
 May 2010
 arXiv:
 arXiv:1005.1240
 Bibcode:
 2010arXiv1005.1240H
 Keywords:

 Mathematics  Number Theory;
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