Results 1 to 10 of about 242 (16)
The Eleventh Power Residue Symbol
Journal of Mathematical Cryptology, 2020 This paper presents an efficient algorithm for computing 11th-power residue symbols in the cyclo-tomic field ℚ(ζ11),$ \mathbb{Q}\left( {{\zeta }_{11}} \right), $where 11 is a primitive 11th root of unity.
Joye Marc +3 more
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Notes on the Quadratic Integers and Real Quadratic Number Fields [PDF]
, 2015 It is shown that when a real quadratic integer $\xi$ of fixed norm $\mu$ is considered, the fundamental unit $\varepsilon_d$ of the field $\mathbb{Q}(\xi) = \mathbb{Q}(\sqrt{d})$ satisfies $\log \varepsilon_d \gg (\log d)^2$ almost always.
Park, Jeongho
core +2 more sources
On Dedekind′s criterion and monogenicity over Dedekind rings
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 71, Page 4455-4464, 2003., 2003 We give a practical criterion characterizing the monogenicity of the integral closure of a Dedekind ring R, based on results on the resultant Res (p, pi) of the minimal polynomial p of a primitive integral element and of its irreducible factors pi modulo prime ideals of R.
M. E. Charkani, O. Lahlou
wiley +1 more source
Constructing elliptic curve isogenies in quantum subexponential time
Journal of Mathematical Cryptology, 2014 Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew +2 more
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Definite orders with locally free cancellation
Transactions of the London Mathematical Society, 2019 We enumerate all orders in definite quaternion algebras over number fields with the Hermite property; this includes all orders with the cancellation property for locally free modules.
Daniel Smertnig, John Voight
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The minimum discriminant of number fields of degree 8 and signature (2,3)
, 2018 In this paper we describe how to use the algorithmic methods provided by Hunter and Pohst in order to give a complete classification of number fields of degree 8 and signature (2,3) with absolute discriminant less than a certain bound. The choice of this
Battistoni, Francesco
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Class numbers of totally real fields and applications to the Weber class number problem
, 2014 The determination of the class number of totally real fields of large discriminant is known to be a difficult problem. The Minkowski bound is too large to be useful, and the root discriminant of the field can be too large to be treated by Odlyzko's ...
Miller, John C.
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Forum of Mathematics, SigmaPursuing ideas in [6], we determine the isometry classes of unimodular lattices of rank $28$ , as well as the isometry classes of unimodular lattices of rank $29$ without nonzero vectors of norm $\leq 2$ .
Bill Allombert, Gaëtan Chenevier
doaj +1 more source
First-degree prime ideals of composite extensions
Journal of Mathematical CryptologyLet Q(α){\mathbb{Q}}\left(\alpha ) and Q(β){\mathbb{Q}}\left(\beta ) be linearly disjoint number fields and let Q(θ){\mathbb{Q}}\left(\theta ) be their compositum.
Santilli Giordano, Taufer Daniele
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A Conjecture Connected with Units of Quadratic Fields [PDF]
, 2012 In this article, we consider the order $\mathcal{O}_{f}={x+yf\sqrt{d}:x,\ y \in \Z}$ with conductor $f\in\N$ in a real quadratic field $K=\mathbb{Q}(\sqrt{d})$ where $d>0$ is square-free and $d\equiv2,3\pmod 4$.
Bircan, Nihal
core