# p-Adic Analogues of the BSD Conjecture and the $$\mathcal {L}$$ -Invariant

Aribam, Chandrakant and Kumar, Narasimha (2019) p-Adic Analogues of the BSD Conjecture and the $$\mathcal {L}$$ -Invariant. The Computational and Theoretical Aspects of Elliptic Curves. pp. 31-44. ISSN 2197-4209

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## Abstract

In this lecture notes, we give an introduction to the p-adic analogues of the Birch and Swinnerton-Dyer conjecture for elliptic curves over Q , when p is a prime of split multiplicative reduction for the elliptic curve. We quickly go through the p-adic methods and the tools from Hida theory, state the exceptional zero conjecture, and give a sketch of the proof of a conjecture of Mazur, Tate and Teitelbaum on the first derivative of p-adic L-functions due to Greenberg and Stevens.

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IITH Creators:
IITH CreatorsORCiD
Kumar, NarasimhaUNSPECIFIED
Item Type: Article
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 26 Dec 2019 09:47