Units groups generated by special values of Siegel modular functions

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In 1976, Coates and Wiles gave large improvement to Birch-Swinnerton-Dyer conjecture for some elliptic curves with complex multiplication by using elliptic units in abelian extensions of imaginary quadratic fields. Main purpose of car investigation is to consider Birch-Swinnerton-Dyer conjecture of the Jacobian variety of some genus-2-curves with complex multiplications.In our investigation, we obtained the following :We put ζ=e^(2πi)/(13) and α=5+5^3+5^9. Then the field k=Q(α) is the CM-fieldcorresponding to the Jacobian variety J(C) of the curve C :y^2=x^5-156x^4+10816x^3-421824x^2+8998912x-8042776.We construct unit groups in abelian extensions of k by special values of Siegel modular functions at a CM-point corresponding to J(C). moreover we write the values of Hecke L-functions associated to the above abelian fields using units given by Siegel modular functions.