On the L-Function of the Curves y2 = x5 + A |
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| Authors: | Stoll Michael; Yang Tonghai |
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| Institution: | School of Engineering and Science, International University Bremen PO Box 75 05 61, 28725 Bremen, Germany, m.stoll{at}iu-bremen.de
Department of Mathematics, University of Wisconsin Madison, WI 53706, USA, thyang{at}math.wisc.edu |
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| Abstract: | Let CA/Q be the curve y2 = x5 + A, and let L(s, JA) denote theL-series of its Jacobian. Under the assumption that the signin the functional equation for L(s, JA) is +1, the criticalvalue L(1, JA) is evaluated in terms of the value of a thetaseries for  depending on Aat a complex multiplication point coming from Q( 5). |
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