Results 11 to 20 of about 2,036 (63)
L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces
Bulletin of the London Mathematical Society, Volume 52, Issue 2, Page 395-409, April 2020., 2020 Abstract We construct non‐trivial L‐equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L‐equivalence for curves (necessarily over non‐algebraically closed fields) and provide a new bit of evidence for the conjectural relationship between L ...
Evgeny Shinder, Ziyu Zhang
wiley +1 more source
Base change for Elliptic Curves over Real Quadratic Fields [PDF]
, 2014 Let E be an elliptic curve over a real quadratic field K and F/K a totally real finite Galois extension. We prove that E/F is modular.Comment: added a short proof of Proposition 2.1 and a few more small changes to improve ...
Dieulefait, Luis, Freitas, Nuno
core +4 more sources
Complete classification of torsion of elliptic curves over quadratic cyclotomic fields [PDF]
, 2010 In a previous paper, the author examined the possible torsions of an elliptic curve over the quadratic fields $\mathbb Q(i)$ and $\mathbb Q(\sqrt{-3})$.
Najman, Filip
core +2 more sources
GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS
Forum of Mathematics, Sigma, 2019 Given an elliptic curve $E$ over $\mathbb{Q}$, a celebrated conjecture of Goldfeld asserts that a positive proportion of its quadratic twists should have analytic rank 0 (respectively 1).
DANIEL KRIZ, CHAO LI
doaj +1 more source
Right triangles with algebraic sides and elliptic curves over number fields [PDF]
, 2009 Given any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem.
Girondo, Ernesto +4 more
core +3 more sources
Torsion of elliptic curves over quadratic cyclotomic fields [PDF]
, 2010 In this paper we study the possible torsions of elliptic curves over $\mathbb Q(i)$ and $\mathbb Q(\sqrt {-3})$.Comment: 9 pages, to appear in Math. J.
Najman, Filip
core +3 more sources
STARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE
Forum of Mathematics, Pi, 2015 Let $E$ be an elliptic curve over $\mathbb{Q}$, and let ${\it\varrho}_{\flat }$ and ${\it\varrho}_{\sharp }$ be odd two-dimensional Artin representations for which ${\it\varrho}_{\flat }\otimes {\it\varrho}_{\sharp }$ is self-dual.
HENRI DARMON, ALAN LAUDER, VICTOR ROTGER
doaj +1 more source
Nonlinearities on particular elliptic curves subspaces and applications
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 Researching on mathematical models for cryptography means to, primary, define the optimal spaces and rules for which we can archive the maximum time to find the involved parameters of the keys and, in the same time, to optimise the time for key ...
Alsaedi Ramzi +2 more
doaj +1 more source
Simplicity of twists of abelian varieties [PDF]
Acta Arith. 171 (2015), no. 1, 15-22, 2013 We give some easy necessary and sufficient criteria for twists of abelian varieties by Artin representations to be simple.
arxiv +1 more source
Open conditions for infinite multiplicity eigenvalues on elliptic curves [PDF]
, 2005 Let E be an elliptic curve defined over a number field K, V the complexification of the group of rational points of E over an algebraic closure L of K, and G the Galois group Gal(L/K).
Im, Bo-Hae, Larsen, Michael
core +6 more sources