Results 11 to 20 of about 15,705,034 (244)
Densities for Elliptic Curves over Global Function Fields
, 2023 Let $K$ be a global function field. We obtain a set of formulas for the densities of the Kodaira types and Tamagawa numbers of elliptic curves over a completion of $K$ that is independent of the field's characteristic. Furthermore, for a finite field $F$ and real numbers $s$ and $ε$ such that $s>1$ and $ε>0$, we prove that there exists a global ...
Yao, Andrew
openaire +3 more sources
Cryptanalysis and improvement of an encryption scheme that uses elliptic curves over finite fields
Maǧallaẗ Al-Kuwayt li-l-ʿulūm, 2021 In this paper, we cryptanalyzed a recently proposed encryption scheme that uses elliptic curves over a finite field. The security of the proposed scheme depends upon the elliptic curve discrete logarithm problem.
Malik Zia Ullah Bashir, R. Ali
semanticscholar +1 more source
Non-monogenic Division Fields of Elliptic Curves [PDF]
, 2020 For various positive integers $n$, we show the existence of infinite families of elliptic curves over $\mathbb{Q}$ with $n$-division fields, $\mathbb{Q}(E[n])$, that are not monogenic, i.e., the ring of integers does not admit a power integral basis.
Hanson Smith
semanticscholar +1 more source
Elliptic Curves Over Finite Fields [PDF]
, 2023 The goal of this thesis is to give an expository report on elliptic curves over finite fields. We begin by giving an overview of the necessary background in algebraic geometry to understand the definition of an elliptic curve. We then explore the general
Calger, Christopher S
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TORSION OF ELLIPTIC CURVES OVER QUADRATIC CYCLOTOMIC FIELDS [PDF]
, 2010 In this paper we study the possible torsions of elliptic curves over ℚ(i) and ℚ(√−3)
Najman, Filip, Filip Najman
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Algebraic divisibility sequences over function fields [PDF]
, 2011 In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields ...
Mahe, Valery +14 more
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Darmon points on elliptic curves over number fields of arbitrary signature [PDF]
, 2014 We present new constructions of complex and p ‐adic Darmon points on elliptic curves over base fields of arbitrary signature. We conjecture that these points are global and present numerical evidence to support our conjecture.
Xavier Guitart +2 more
semanticscholar +1 more source
Torsion groups of a family of elliptic curves over number fields [PDF]
, 2019 summary:We compute the torsion group explicitly over quadratic fields and number fields of degree coprime to 6 for a family of elliptic curves of the form $E\colon y^2 = x^3 +c$, where $c$ is an ...
Dey, Pallab Kanti
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Multiplication polynomials and relative Manin-Mumford [PDF]
, 2015 After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is $(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the ...
Schmidt, Harry
core +1 more source
Torsion points on elliptic curves over function fields and a theorem of Igusa [PDF]
, 2008 If F is a global function field of characteristic p > 3 , we employ Tate's theory of analytic uniformization to give an alternative proof of a theorem of Igusa describing the image of the natural Galois representation on torsion points of non-isotrivial ...
A. Bandini, I. Longhi, S. Vigni
semanticscholar +1 more source