Trivial zeros of $p$ -adic $L$ -functions at near-central points
By D. Benois. Journal of the Institute of Mathematics of Jussieu, 2011
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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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d43a938b54eb25d920d1af87deea44e4e9b65677
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In Algebra and Number Theory
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Citations in the corpus
- Analytic families of finite-slope Selmer groups (2013, background): “…= ker[H1(G, D)→ H1(G, D/F+)], which is a generalization of the (strict) ordinary local subspace studied by Greenberg [1994b] in conjunction with the nonstrict ordinary local subspace (introduced earlier in [Greenberg 1989; 1994a]) ker [ H1(G K , D)→ H1 ( G K̂ unr, (D/F +)⊗B†rig,K B† rig,K̂ unr )] .”