1 Ocak 2016 Dergi makalesi Açık Erişim

Buyukboduk, Kazim

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    <subfield code="a">Let E/Q be an elliptic curve which has split multiplicative reduction at a prime p and whose analytic rank r(an)(E) equals one. The main goal of this article is to relate the second-order derivative of the Mazur-Tate-Teitelbaum p-adic L-function L-p(E, s) of E to Nekovr's height pairing evaluated on natural elements arising from the Beilinson-Kato elements. Along the way, we extend a Rubin-style formula of Nekovar to apply in the presence of exceptional zeros. Our height formula allows us, among other things, to compare the order of vanishing of L-p(E, s) at s = 1 with its (complex) analytic rank ran(E) assuming the non-triviality of the height pairing. This has consequences toward a conjecture of Mazur, Tate, and Teitelbaum.</subfield>
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    <subfield code="a">10.1093/imrn/rnv205</subfield>
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    <subfield code="a">On Nekovar's Heights, Exceptional Zeros and a Conjecture of Mazur-Tate-Teitelbaum</subfield>
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