Results 11 to 20 of about 1,082,587 (269)

Short Principal Ideal Problem in multicubic fields

Journal of Mathematical Cryptology, 2020
One family of candidates to build a post-quantum cryptosystem upon relies on euclidean lattices. In order to make such cryptosystems more efficient, one can consider special lattices with an additional algebraic structure such as ideal lattices.
Lesavourey Andrea, Plantard Thomas, Susilo Willy   +2 more
doaj   +1 more source

On Hilbert class field tower for some quartic number fields [PDF]

Arab Journal of Mathematical Sciences, 2021
We determine the Hilbert 2-class field tower for some quartic number fields k whose 2-class group Ck,2 is isomorphic to ℤ/2ℤ×ℤ/2ℤ.
Abdelmalek Azizi, Mohamed Talbi, Mohammed Talbi   +2 more
doaj   +1 more source

Semicircular elements induced by p-adic number fields [PDF]

Opuscula Mathematica, 2017
In this paper, we study semicircular-like elements, and semicircular elements induced by \(p\)-adic analysis, for each prime \(p\). Starting from a \(p\)-adic number field \(\mathbb{Q}_{p}\), we construct a Banach \(*\)-algebra \(\mathfrak{LS}_{p}\), for
Ilwoo Cho, Palle E. T. Jorgensen
doaj   +1 more source

Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields

Mathematics, 2022
For a given integer n, we provide some families of imaginary quadratic number fields of the form Q(4q2−pn), whose ideal class group has a subgroup isomorphic to Z/nZ.
Kwang-Seob Kim
doaj   +1 more source

The Genus Field and Genus Number in Algebraic Number Fields [PDF]

Nagoya Mathematical Journal, 1967
Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.
openaire   +2 more sources

A generalization of arithmetic derivative to p-adic fields and number fields [PDF]

Notes on Number Theory and Discrete Mathematics
The arithmetic derivative is a function from the natural numbers to itself that sends all prime numbers to 1 and satisfies the Leibniz rule. The arithmetic partial derivative with respect to a prime p is the p-th component of the arithmetic derivative ...
Brad Emmons, Xiao Xiao
doaj   +1 more source

Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$ [PDF]

Mathematica Bohemica, 2021
If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prime of the form $4+n^2$, we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q{\mathcal O}_K$, where $q$ is a positive rational
Julio Pérez-Hernández, Mario Pineda-Ruelas   +1 more
doaj   +1 more source

Class Number and Ramification in Number Fields [PDF]

Nagoya Mathematical Journal, 1963
In the ring Ok of algebraic integers of a number field K the group Ik of ideals of Ok modulo the subgroup Pk of principal ideals is a finite abelian group of order hk, the class number of K. The determination of this number is an outstanding problem of algebraic number theory.
Brumer, Armand, Rosen, Michael
openaire   +2 more sources

Norms in finite galois extensions of the rationals

International Journal of Mathematics and Mathematical Sciences, 1990
We show that under certain conditions a rational number is a norm in a given finite Galois extension of the rationals if and only if this number is a local norm at a certain finite number of places in a certain finite abelian extension of the rationals.
Hans Opolka
doaj   +1 more source

On dynamical systems induced by p-adic number fields [PDF]

Opuscula Mathematica, 2015
In this paper, we construct dynamical systems induced by \(p\)-adic number fields \(\mathbb{Q}_{p}\). We study the corresponding crossed product operator algebras induced by such dynamical systems.
Ilwoo Cho
doaj   +1 more source