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Trivial zeros of $p$-adic $L$-functions at near-central points

Published online by Cambridge University Press:  24 September 2013

Denis Benois*
Affiliation:
Institut de Mathématiques de Bordeaux, UMR 5251, Université de Bordeaux, 351 cours de la Libération, F-33400 Talence, France (denis.benois@math.u-bordeaux1.fr)

Abstract

Using the $\ell $-invariant constructed in our previous paper we prove a Mazur–Tate–Teitelbaum-style formula for derivatives of $p$-adic $L$-functions of modular forms at trivial zeros. The novelty of this result is to cover the near-central point case. In the central point case our formula coincides with the Mazur–Tate–Teitelbaum conjecture proved by Greenberg and Stevens and by Kato, Kurihara and Tsuji at the end of the 1990s.

Type
Research Article
Copyright
©Cambridge University Press 2013 

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