Browsing by Author "Rotger Cerdà, Víctor"

Algorithms for chowheegner points via iterated integrals
Darmon, Henri; Daub, Michael; Lichtenstein, Sam; Rotger Cerdà, Víctor (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 CerednikDrinfeld primes
Molina Blanco, Santiago; Rotger Cerdà, Víctor (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 CerednikDrinfeld’s integral model at a prime of bad reduction and its sets ... 
BeilinsonFlach elements and Euler systems II: padic families and the Birch and SwinnertonDyer conjecture
Bertolini, Massimo; Darmon, Henri; Rotger Cerdà, Víctor (20150323)
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 SwinnertonDyer conjecture in analytic rank zero for the HasseWeilArtin Lseries ... 
BeilinsonFlach elements and Euler systems I: syntomic regulators and padic Rankin Lseries
Bertolini, Massimo; Darmon, Henri; Rotger Cerdà, Víctor (2015)
Article
Open AccessThis article is the first in a series devoted to the Euler system arising from padic families of BeilinsonFlach elements in the first Kgroup of the product of two modular curves. It relates the image of these elements ... 
BeilinsonFlach elements, Stark units and padic iterated integrals
Rivero Salgado, Óscar; Rotger Cerdà, Víctor (20190814)
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 SwinnertonDyer conjecture for HasseWeilArtin Lfunctions
Darmon, Henri; Rotger Cerdà, Víctor (20170701)
Article
Open AccessThis article establishes new cases of the Birch and SwinnertonDyer conjecture in analytic rank 0, for elliptic curves over $ \mathbb{Q}$ viewed over the fields cut out by certain selfdual Artin representations of dimension ... 
Elliptic curves of rank two and generalized Kato classes
Darmon, Henri; Rotger Cerdà, Víctor (20160824)
Article
Open AccessHeegner points play an outstanding role in the study of the Birch and SwinnertonDyer conjecture, providing canonical Mordell–Weil generators whose heights encode first derivatives of the associated Hasse–Weil Lseries. ... 
GrossStark units and padic iterated integrals attached to modular forms of weight one
Darmon, Henri; Lauder, Alan; Rotger Cerdà, Víctor (20160801)
Article
Open AccessThis article can be read as a companion and sequel to the authors’ earlier article on Stark points and padic iterated integrals attached to modular forms of weight one, which proposes a conjectural expression for the ... 
Heegner points on HijikataPizerShemanske curves and the Birch and SwinnertonDyer conjecture
Longo, Matteo; Rotger Cerdà, Víctor; Vera Piquero, Carlos de (20180101)
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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
Darmon, Henri; Lauder, Alan; Rotger Cerdà, Víctor (20151001)
Article
Restricted access  publisher's policyThis article examines the Fourier expansions of certain nonclassical padic modular forms of weight one: the eponymous generalised eigertforms of the title, so called because they lie in a generalised eigenspace for the ... 
SatoTate distributions and Galois endomorphism modules in genus 2
Fité, Francesc; Kedlaya, Kiran; Rotger Cerdà, Víctor; Sutherland, Andrew (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 Lfunction of A. This distribution is expected to correspond to taking characteristic poly nomials ... 
Stark points and padic iterated integrals attached to modular forms of weight one
Darmon, Henri; Lauder, Alan; Rotger Cerdà, Víctor (Cambridge University Press, 20150101)
Article
Open AccessLet be an elliptic curve over , and let and be odd twodimensional Artin representations for which is selfdual. The progress on modularity achieved in recent decades ensures the existence of normalized eigenforms , , and ... 
Stark points and the HidaRankin padic Lfunction
Casazza, Daniele; Rotger Cerdà, Víctor (201802)
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 padic avatar of the leading term at s=1 of the Hasse–Weil–Artin ...