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Algebraic leaves of algebraic foliations over number fields [PDF]

Publications mathématiques de l'IHÉS, 2001
This paper proves an algebraicity criterion for leaves of algebraic foliations over number fields. Let \(K\) be a number field embedded in \(\mathbb C\), let \(X\) be a smooth algebraic variety over \(K\) (i.e., an integral separated scheme of finite type over \(K\)), and let \(F\) be an algebraic subbundle of the tangent bundle \(T_X\). We assume that
Bost, Jean-Benoît
core   +4 more sources

Gr\"obner Bases over Algebraic Number Fields [PDF]

Proceedings of the 2015 International Workshop on Parallel Symbolic Computation, 2015
Although Buchberger's algorithm, in theory, allows us to compute Gr\"obner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field.
Boku, Dereje Kifle, Decker, Wolfram, Fieker, Claus, Steenpass, Andreas   +3 more
core   +2 more sources

A counterexample to 'Algebraic function fields with small class number' [PDF]

, 2013
I give a counter example of function field over GF(2) of genus 4 with class number one.
Stirpe, Claudio
core   +3 more sources

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.
Yoshiomi Furuta
openaire   +3 more sources

Normal Algebraic Number Fields [PDF]

Proceedings of the National Academy of Sciences, 1940
MacLane, Saunders, Schilling, O. F. G.
openaire   +5 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

Finiteness theorems for algebraic tori over function fields

Comptes Rendus. Mathématique, 2021
We present a number of finiteness results for algebraic tori (and, more generally, for algebraic groups with toric connected component) over two classes of fields: finitely generated fields and function fields of algebraic varieties over fields of type ...
Rapinchuk, Andrei S., Rapinchuk, Igor A.
doaj   +1 more source

Some Properties of Euler’s Function and of the Function τ and Their Generalizations in Algebraic Number Fields

Mathematics, 2021
In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function τ, and the generalized function τ in algebraic number fields.
Nicuşor Minculete, Diana Savin
doaj   +1 more source

About the Entropy of a Natural Number and a Type of the Entropy of an Ideal

Entropy, 2023
In this article, we find some properties of certain types of entropies of a natural number. We are studying a way of measuring the “disorder” of the divisors of a natural number. We compare two of the entropies H and H¯ defined for a natural number.
Nicuşor Minculete, Diana Savin
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