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ON THE L-FUNCTION OF THE CURVES $\lowercase{y}^2 = \lowercase{x}^5 + A$
Published online by Cambridge University Press: 25 September 2003
Abstract
Let $C_A/\Q$ be the curve $y^2 = x^5 + A$, and let $L(s, J_A)$ denote the $L$-series of its Jacobian. Under the assumption that the sign in the functional equation for $L(s, J_A)$ is $+1$, the critical value $L(1, J_A)$ is evaluated in terms of the value of a theta series for $\Q(\sqrt{5})$ depending on $A$ at a complex multiplication point coming from $\Q(\zeta_5)$.
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- The London Mathematical Society 2003
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