TN - Teoria de Nombres
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Articles de revista [63]
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7demates: memòria: curs 2017-18
(2018-07)
External research report
Open Access -
Report: Temps de... STEM
(2018-05-22)
External research report
Open AccessLa ciència en acció és, ara més que mai, STEM, de manera que "Temps de ...STEM" és una fórmula d'actualitat: integra ciència i cultura, establint ponts entre públic de totes edats i professorat de tots nivells, des d'infantil ... -
Fields of definition of elliptic k-curves and the realizability of all genus 2 sato–tate groups over a number field
(2018-07-01)
Article
Open AccessLet A/Q be an abelian variety of dimension g = 1 that is isogenous over Q to Eg, where E is an elliptic curve. If E does not have complex multiplication (CM), by results of Ribet and Elkies concerning fields of definition ... -
Del Pezzo surfaces over finite fields and their Frobenius traces
(2018-04-10)
Article
Open AccessLet S be a smooth cubic surface over a finite field q. It is known that #S( q) = 1 + aq + q2 for some a ¿ {-2, -1, 0, 1, 2, 3, 4, 5, 7}. Serre has asked which values of a can arise for a given q. Building on special cases ... -
Hopf Galois structures on symmetric and alternating extensions
(2018)
Article
Open AccessBy using a recent theorem by Koch, Kohl, Truman and Underwood on normality, we determine that some types of Hopf Galois structures do not occur on Galois extensions with Galois group isomorphic to alternating or symmetric ... -
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 ... -
Computation of numerical semigroups by means of seeds
(2018-09-01)
Article
Open AccessFor the elements of a numerical semigroup which are larger than the Frobenius number, we introduce the definition of seed by broadening the notion of generator. This new concept allows us to explore the semigroup tree in ... -
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 ... -
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 ... -
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 ... -
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. ... -
On the rank and the convergence rate toward the Sato-Tate measure
(2017-10-16)
Article
Open AccessLet A be an abelian variety defined over a number field and let G denote its Sato–Tate group. Under the assumption of certain standard conjectures on L -functions attached to the irreducible representations of G, we study ...
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