Results 11 to 20 of about 4,819,757 (284)

Super-multiplicativity of ideal norms in number fields [PDF]

, 2020
In this article we study inequalities of ideal norms. We prove that in a subring $R$ of a number field every ideal can be generated by at most $3$ elements if and only if the ideal norm satisfies $N(IJ) \geq N(I)N(J)$ for every pair of non-zero ideals $I$
Marseglia, Stefano
core   +3 more sources

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

Machine-learning number fields

Mathematics, Computation and Geometry of Data, 2022
20 pages, 1 figure, 3 ...
He, Yang-Hui, Lee, Kyu-Hwan, Oliver, Thomas   +2 more
openaire   +2 more sources

Jacobi forms over number fields from linear codes

AIMS Mathematics, 2022
We suggest a Jacobi form over a number field $ \Bbb Q(\sqrt 5, i) $; for obtaining this, we use a linear code $ C $ over $ R: = \Bbb F_4+u\Bbb F_4 $, where $ u^2 = 0 $.
Boran Kim, Chang Heon Kim, Soonhak Kwon, Yeong-Wook Kwon   +3 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

Number Fields [PDF]

, 2023
Number Fields is a textbook for algebraic number theory. It grew out of lecture notes of master courses taught by the author at Radboud University, the Netherlands, over a period of more than four decades. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory.
openaire   +1 more source

Bounded gaps between primes in number fields and function fields [PDF]

, 2014
The Hardy--Littlewood prime $k$-tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs of Zhang, Maynard, and Tao have nevertheless made significant progress ...
Castillo, Abel, Hall, Chris, Oliver, Robert J. Lemke, Pollack, Paul, Thompson, Lola   +4 more
core   +2 more sources

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

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