Now showing items 1-16 of 16

• #### Algorithms for chow-heegner points via iterated integrals ﻿

(2015)
Article
Restricted access - publisher's policy
Let E/Q be an elliptic curve of conductor N and let f be the weight 2 newform on G0(N) associated to it by modularity. Building on an idea of S. Zhang, an article by Darmon, Rotger, and Sols describes the construction of ...
• #### Automorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes ﻿

(2014)
Article
Open Access
The aim of this short note is to show how the interplay of the action of the automorphism group of a Shimura curve on the special fiber of its Cerednik-Drinfeld’s integral model at a prime of bad reduction and its sets ...
• #### Beilinson-Flach elements and Euler systems I: syntomic regulators and p-adic Rankin L-series ﻿

(2015)
Article
Open Access
This article is the first in a series devoted to the Euler system arising from p-adic families of Beilinson-Flach elements in the first K-group of the product of two modular curves. It relates the image of these elements ...
• #### Beilinson-Flach elements and Euler systems II: p-adic families and the Birch and Swinnerton-Dyer conjecture ﻿

(2015-03-23)
Article
Open Access
Let E be an elliptic curve over Q and let % be an odd, irreducible twodimensional Artin representation. This article proves the Birch and Swinnerton-Dyer conjecture in analytic rank zero for the Hasse-WeilArtin L-series ...
• #### Beilinson-Flach elements, Stark units and p-adic iterated integrals ﻿

(2019-08-14)
Article
Open Access
We study weight one specializations of the Euler system of Beilinson–Flach elements introduced by Kings, Loeffler and Zerbes, with a view towards a conjecture of Darmon, Lauder and Rotger relating logarithms of units in ...
• #### Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions ﻿

(2017-07-01)
Article
Open Access
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-dual Artin representations of dimension ...
• #### Elliptic curves of rank two and generalized Kato classes ﻿

(2016-08-24)
Article
Open Access
Heegner points play an outstanding role in the study of the Birch and Swinnerton-Dyer conjecture, providing canonical Mordell–Weil generators whose heights encode first derivatives of the associated Hasse–Weil L-series. ...
• #### Gross-Stark units and p-adic iterated integrals attached to modular forms of weight one ﻿

(2016-08-01)
Article
Open Access
This article can be read as a companion and sequel to the authors’ earlier article on Stark points and p-adic iterated integrals attached to modular forms of weight one, which proposes a conjectural expression for the ...
• #### Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture ﻿

(2018-01-01)
Article
Open Access
We study Heegner points on elliptic curves, or more generally modular abelian varieties, coming from uniformization by Shimura curves attached to a rather general type of quaternionic orders. We address several questions ...
• #### Heegner points, Stark-Heegner points and diagonal classes ﻿

(2020-02-03)
Book
Restricted access - publisher's policy
• #### On rigid analytic uniformizations of Jacobians of Shimura curves ﻿

(2012)
Article
Open Access
The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed ...
• #### On the elliptic Stark conjecture at primes of multiplicative reduction ﻿

(2019-01-01)
Article
Open Access
In [DLR], Darmon, Lauder, and Rotger formulated a p-adic elliptic Stark conjecture for the twist of an elliptic curve E/Q by the self-dual tensor product ¿ ¿ of two odd and two-dimensional Artin representations. These ...
• #### Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields ﻿

(2015-10-01)
Article
Restricted access - publisher's policy
This article examines the Fourier expansions of certain non-classical p-adic modular forms of weight one: the eponymous generalised eigertforms of the title, so called because they lie in a generalised eigenspace for the ...
• #### Sato-Tate distributions and Galois endomorphism modules in genus 2 ﻿

(2012)
Article
Restricted access - publisher's policy
For an abelian surface A over a number eld k, we study the limit- ing distribution of the normalized Euler factors of the L-function of A. This distribution is expected to correspond to taking characteristic poly- nomials ...
• #### Stark points and p-adic iterated integrals attached to modular forms of weight one ﻿

(Cambridge University Press, 2015-01-01)
Article
Open Access
Let be an elliptic curve over , and let and be odd two-dimensional Artin representations for which is self-dual. The progress on modularity achieved in recent decades ensures the existence of normalized eigenforms , , and ...
• #### Stark points and the Hida-Rankin p-adic L-function ﻿

(2018-02)
Article
Open Access
This article is devoted to the elliptic Stark conjecture formulated by Darmon (Forum Math Pi 3:e8, 2015), which proposes a formula for the transcendental part of a p-adic avatar of the leading term at s=1 of the Hasse–Weil–Artin ...