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
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
Affine Sergeev Algebra and q‐Analogues of the Young Symmetrizers for Projective Representations of the Symmetric Group [PDF]
, 1997 We study a q‐deformation for the crossed product of the symmetric group Sn with the Clifford algebra on n anticommuting generators. We obtain a q‐version of the projective analogue for the classical Young symmetrizer introduced by the second author.
A. Jones, M. Nazarov
semanticscholar +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
CODIMENSION TWO CYCLES IN IWASAWA THEORY AND ELLIPTIC CURVES WITH SUPERSINGULAR REDUCTION
Forum of Mathematics, Sigma, 2019 A result of Bleher, Chinburg, Greenberg, Kakde, Pappas, Sharifi and Taylor has initiated the topic of higher codimension Iwasawa theory. As a generalization of the classical Iwasawa main conjecture, they prove a relationship between analytic objects (a ...
ANTONIO LEI, BHARATHWAJ PALVANNAN
doaj +1 more source
COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES
Forum of Mathematics, Sigma, 2016 Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
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On Serre's uniformity conjecture for semistable elliptic curves over totally real fields [PDF]
, 2015 Let $K$ be a totally real field, and let $S$ be a finite set of non-archimedean places of $K$. It follows from the work of Merel, Momose and David that there is a constant $B_{K,S}$ so that if $E$ is an elliptic curve defined over $K$, semistable outside
Anni, Samuele, Siksek, Samir
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On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1
Proceedings of the London Mathematical Society, Volume 118, Issue 5, Page 1245-1276, May 2019., 2019 Abstract The main result of this paper is to extend from Q to each of the nine imaginary quadratic fields of class number 1 a result of [Serre, Duke Math. J. 54 (1987) 179–230] and [Mestre–Oesterlé, J. reine. angew. Math. 400 (1989) 173–184], namely that if E is an elliptic curve of prime conductor, then either E or a 2‐, 3‐ or 5‐isogenous curve has ...
John Cremona, Ariel Pacetti
wiley +1 more source
, 2018 We prove that there exist infinitely many rationals a, b and c with the property that a^2-1, b^2-1, c^2-1, ab-1, ac-1 and bc-1 are all perfect squares.
Dujella, Andrej +3 more
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Torsion points with multiplicatively dependent coordinates on elliptic curves
, 2020 In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations.
Barroero, Fabrizio, Sha, Min
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