Browsing by Author "Rotger Cerdà, Víctor"
Now showing items 1-13 of 13
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Algorithms for chow-heegner points via iterated integrals
(2015)
Article
Restricted access - publisher's policyLet 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 AccessThe 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 II: p-adic families and the Birch and Swinnerton-Dyer conjecture
(2015-03-23)
Article
Open AccessLet 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 and Euler systems I: syntomic regulators and p-adic Rankin L-series
(2015)
Article
Open AccessThis 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, Stark units and p-adic iterated integrals
(2019-08-14)
Article
Open AccessWe 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 AccessThis 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 AccessHeegner 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 AccessThis 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 AccessWe 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 ... -
Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields
(2015-10-01)
Article
Restricted access - publisher's policyThis 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 policyFor 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 AccessLet 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 AccessThis 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 ...
