Abstract
Given an elliptic curve E and a prime p of (good) supersingular reduction, we formulate p-adic analogues of the Birch and Swinnerton-Dyer conjecture using a pair of Iwasawa functions L♯(E,T) and L♭(E,T). They are equivalent to the conjectures of Perrin-Riou and Bernardi. We also generalize work of Kurihara and Pollack to give a criterion for positive rank in terms of the value of the quotient between these functions, and derive a result towards a non-vanishing conjecture. We also generalize a conjecture of Kurihara and Pollack concerning the greatest common divisor of the two functions to the general supersingular case.
Original language | English (US) |
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Article number | 17 |
Journal | Research in Number Theory |
Volume | 1 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1 2015 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
Keywords
- Birch and Swinnerton-Dyer conjecture
- Iwasawa theory
- p-adic l-functions