Trivial Zeros of $p$-adic $L$-Functions at Near-Central Points

Denis Benois (1)

1 IMB - Institut de Mathématiques de Bordeaux

Using the L-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.

Domaines: Théorie des nombres [math.NT]

Denis Benois. Trivial Zeros of $p$-adic $L$-Functions at Near-Central Points. Journal of the Institute of Mathematics of Jussieu, 2014, 13 (3), pp.561-598. ⟨10.1017/S1474748013000261⟩. ⟨hal-00992320⟩