Results 1 to 10 of about 366 (21)
Characterization of the numbers which satisfy the height reducing property
, 2014 Let $\alpha$ be a complex number. We show that there is a finite subset $F$ of the ring of the rational integers $\mathbb{Z}$, such that $F\left[ \alpha\right] =\mathbb{Z}\left[ \alpha\right]$, if and only if $\alpha$ is an algebraic number whose ...
Akiyama, Shigeki +2 more
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On Mertens-Ces\`aro Theorem for Number Fields
, 2015 Let $K$ be a number field with ring of integers $\mathcal O$. After introducing a suitable notion of density for subsets of $\mathcal O$, generalizing that of natural density for subsets of $\mathbb Z$, we show that the density of the set of coprime $m ...
Ferraguti, Andrea, Micheli, Giacomo
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Reciprocal Monogenic Septinomials of Degree 2n3
Annales Mathematicae SilesianaeWe prove a new irreducibility criterion for certain septinomials in ℤ[x], and we use this result to construct infinite families of reciprocal septinomials of degree 2n3 that are monogenic for all n ≥ 1.
Jones Lenny
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The product of a quartic and a sextic number cannot be octic
Open MathematicsIn this article, we prove that the product of two algebraic numbers of degrees 4 and 6 over Q{\mathbb{Q}} cannot be of degree 8. This completes the classification of so-called product-feasible triplets (a,b,c)∈N3\left(a,b,c)\in {{\mathbb{N}}}^{3} with a ...
Dubickas Artūras, Maciulevičius Lukas
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An elementary approach to toy models for D. H. Lehmer's conjecture
, 2010 In 1947, Lehmer conjectured that the Ramanujan's tau function $\tau (m)$ never vanishes for all positive integers $m$, where $\tau (m)$ is the $m$-th Fourier coefficient of the cusp form $\Delta_{24}$ of weight 12.
B. B. Venkov +8 more
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Hasse-Minkowski theorem for quadratic forms on Mordell-Weil type groups
, 2017 In this paper we investigate an analogue of Hasse-Minkowski theorem for quadratic forms on Mordell-Weil type groups over number fields like $S$-units, abelian varieties with trivial ring of endomorphisms and odd algebraic $K$-theory ...
Barańczuk, Stefan
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Unit groups of some multiquadratic number fields and 2-class groups. [PDF]
Period Math Hung, 2022 Chems-Eddin MM.
europepmc +1 more source
Geometry of integers revisited
, 2019 We study geometry of the ring of algebraic integers $O_K$ of a number field $K$. Namely, it is proved that the inclusion $\mathbf{Z}\subset O_K$ defines a covering of the Riemann sphere $\mathbf{C}P^1$ ramified over three points $\{0,1,\infty\}$.
Nikolaev, Igor
core
On the distribution of multiplicatively dependent vectors
, 2019 In this paper, we study the distribution of multiplicatively dependent vectors. For example, although they have zero Lebesgue measure, they are everywhere dense both in $\R^n$ and $\C^n$.
Sha, Min +2 more
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Clinical Performance and Safety of 108 SpineJack Implantations: 1-Year Results of a Prospective Multicentre Single-Arm Registry Study. [PDF]
Biomed Res Int, 2015 Noriega D +14 more
europepmc +1 more source