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Journal of the London Mathematical Society 2003 68(2):273-287; doi:10.1112/S0024610703004460
© 2003 by London Mathematical Society
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© The London Mathematical Society

On the L-Function of the Curves y2 = x5 + A

Michael Stoll and Tonghai Yang

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

Received 9 July 2001. Revision received 24 September 2002.

Let CA/Q be the curve y2 = x5 + A, and let L(s, JA) denote the L-series of its Jacobian. Under the assumption that the sign in the functional equation for L(s, JA) is +1, the critical value L(1, JA) is evaluated in terms of the value of a theta series for Formula depending on A at a complex multiplication point coming from Q({zeta}5).


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