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We construct three-variable $ p $-adic families of Galois cohomology classes attached to
Rankin convolutions of modular forms, and prove an explicit reciprocity law relating these …

Let A be an abelian variety over a number field K. An identity between the L-functions L (A/K
i, s) for extensions K i of K induces a conjectural relation between the Birch-Swinnerton-Dyer …

In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to
Rankin–Selberg products of conjugate self-dual automorphic representations, within the …

For elliptic curves over $\mathbb {Q} $, we prove the $ p $-indivisibility of derived Heegner
points for certain prime numbers $ p $, as conjectured by Kolyvagin in 1991. Applications …

Abstract Let E∕ ℚ be an elliptic curve of conductor N, let p> 3 be a prime where E has good
ordinary reduction, and let K be an imaginary quadratic field satisfying the Heegner …

This article establishes new cases of the Birch and Swinnerton-Dyer conjecture in analytic
rank $0 $, for elliptic curves over $\mathbb {Q} $ viewed over the fields cut out by certain self …

We prove the μ-part of the main conjecture for modular forms along the anticyclotomic Zp-
extension of a quadratic imaginary field. Our proof consists of first giving an explicit formula …

Explicit Gross–Zagier and Waldspurger formulae Page 1 Algebra & Number Theory msp
Volume 8 2014 No. 10 Explicit Gross–Zagier and Waldspurger formulae Li Cai, Jie Shu and …

In this article, we generalize some works of Bertolini–Darmon and Vatsal on anticyclotomic L-
functions attached to modular forms of weight two to higher weight case. We construct a …