On the Lfunctions of the curves y2 = x + A
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Let > 3 be an odd prime and let A be an integer not divisible by . Let CA be the non-singular projective model over of the affine curve CA: y2= x+ A. In this paper, we use the theory of Hilbert modular Eisenstein series to obtain a formula for the central value of the Hasse-Weil L-function L(CA, s) of the curve CA when the cyclotomic field () has ideal class number 1. 2008 London Mathematical Society.