Author： Pál Ambrus
Publisher： Springer Publishing Company
ISSN： 0025-5874
Source： Mathematische Zeitschrift, Vol.254, Iss.3, 2006-11, pp. : 461-483
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Abstract
Based on the analogy between number fields and function fields of one variable over finite fields, we formulate and prove an analogue of the exceptional zero conjecture of Mazur, Tate and Teitelbaum for elliptic curves defined over function fields. The proof uses modular parametrization by Drinfeld modular curves and the theory of non-archimedean integration. As an application we prove a refinement of the Birch-Swinnerton-Dyer conjecture if the analytic rank of the elliptic curve is zero.
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