Results 11 to 20 of about 255 (28)

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

Exceptional units and Euclidean number fields [PDF]

, 2018
.: By a result of H.W. Lenstra, one can prove that a number field is Euclidean with the aid of exceptional units. We describe two methods computing exceptional sequences, i.e., sets of units such that the difference of any two of them is still a unit ...
Houriet, Julien
core   +1 more source

Irregular primes and cyclotomic invariants to four million

, 1993
Recent computations of irregular primes, and associated cyclotomic invariants, were extended to all primes below four million using an enhanced multisectioning/convolution method.
J. Buhler, R. Crandall, R. Ernvall, T. Metsänkylä   +3 more
semanticscholar   +1 more source

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
core   +1 more source

Computations of Galois Representations Associated to Modular Forms

, 2014
We propose an improved algorithm for computing mod $\ell$ Galois representations associated to a cusp form $f$ of level one. The proposed method allows us to explicitly compute the case with $\ell=29$ and $f$ of weight $k=16$, and the cases with $\ell=31$
Tian, Peng
core   +1 more source

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.
core   +1 more source

On the quantum security of high-dimensional RSA protocol

Journal of Mathematical Cryptology
The idea of extending the classical RSA protocol using algebraic number fields was introduced by Takagi and Naito (Construction of RSA cryptosystem over the algebraic field using ideal theory and investigation of its security.
Rahmani Nour-eddine, Serraj Taoufik, Ismaili Moulay Chrif, Azizi Abdelmalek   +3 more
doaj   +1 more source

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  

Configuration of the Crucial Set for a Quadratic Rational Map

, 2015
Let $K$ be a complete, algebraically closed non-archimedean valued field, and let $\varphi(z) \in K(z)$ have degree two. We describe the crucial set of $\varphi$ in terms of the multipliers of $\varphi$ at the classical fixed points, and use this to show
Doyle, John R., Jacobs, Kenneth, Rumely, Robert   +2 more
core   +1 more source

First-degree prime ideals of composite extensions

Journal of Mathematical Cryptology
Let 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
doaj   +1 more source