Results 1 to 10 of about 11,325,403 (303)

A database of number fields [PDF]

LMS Journal of Computation and Mathematics, 2014
AbstractWe describe an online database of number fields which accompanies this paper. The database centers on complete lists of number fields with prescribed invariants. Our description here focuses on summarizing tables and connections to theoretical issues of current interest.
Jones, John W., Roberts, David P.
openaire   +7 more sources

Redefining topological robustness in optical polarization fields through a generalized skyrmion number [PDF]

Nature Communications
Skyrmions are important topologically non-trivial fields characteristic of models spanning scales from the microscopic to the cosmological. However, the skyrmion number can only be defined for fields with specific boundary conditions, limiting its use in
An Aloysius Wang, Yifei Ma, Zimo Zhao, Yuxi Cai, Stephen M. Morris, Honghui He, Zhenwei Xie, Peng Shi, Yijie Shen, Anatoly V. Zayats, Xiaocong Yuan, Chao He   +11 more
doaj   +2 more sources

Root lattices in number fields

Bulletin of Mathematical Sciences, 2021
We explore whether a root lattice may be similar to the lattice 𝒪 of integers of a number field K endowed with the inner product (x,y) := TraceK/ℚ(x ⋅ 𝜃(y)), where 𝜃 is an involution of K.
Vladimir L. Popov, Yuri G. Zarhin
doaj   +1 more source

Torsion subgroups of rational Mordell curves over some families of number fields

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
Mordell curves over a number field K are elliptic curves of the form y2 = x3 + c, where c ∈ K \ {0}. Let p ≥ 5 be a prime number, K a number field such that [K : ℚ] ∈ {2p, 3p}.
Gužvić Tomislav, Roy Bidisha
doaj   +1 more source

The number field sieve [PDF]

Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90, 1990
The number field sieve is an algorithm to factor integers of the form re − s for small positive r and |s|. The algorithm depends on arithmetic in an algebraic number field. We describe the algorithm, discuss several aspects of its implementation, and present some of the factorizations obtained.
Lenstra, Arjen K., Lenstra, H. W. Jr, Manasse, M. S., Pollard, J. M.   +3 more
openaire   +3 more sources

Gauss Congruences in Algebraic Number Fields

Annales Mathematicae Silesianae, 2022
In this miniature note we generalize the classical Gauss congruences for integers to rings of integers in algebraic number fields.
Gładki Paweł, Pulikowski Mateusz
doaj   +1 more source

Point counting for foliations over number fields

Forum of Mathematics, Pi, 2022
Let${\mathbb M}$ be an affine variety equipped with a foliation, both defined over a number field ${\mathbb K}$. For an algebraic $V\subset {\mathbb M}$ over ${\mathbb K}$, write $\delta _{V}$ for the maximum of the degree and log-height of V.
Gal Binyamini
doaj   +1 more source

Constructions of Dense Lattices of Full Diversity

Trends in Computational and Applied Mathematics, 2020
A lattice construction using Z-submodules of rings of integers of number fields is presented. The construction yields rotated versions of the laminated lattices A_n for n = 2,3,4,5,6, which are the densest lattices in their respective dimensions.
A. A. Andrade, A. J. Ferrari, J. C. Interlando, R. R. Araujo   +3 more
doaj   +1 more source

Ternary number systems in finite fields [PDF]

Компьютерная оптика, 2018
The work continues the author's previous study of positional number systems in finite fields. The paper considers ternary number systems and arithmetic operations algorithms for the representation of elements of finite fields in the so-called ternary ...
Vladimir Chernov
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