Results 11 to 20 of about 410 (42)
A sharp result on m-covers [PDF]
, 2005 Let A={a_s+n_sZ}_{s=1}^k be a finite system of arithmetic sequences which forms an m-cover of Z (i.e., every integer belongs at least to m members of A). In this paper we show the following sharp result: For any positive integers m_1,...,m_k and theta in
Pan, Hao, Sun, Zhi-Wei
core +5 more sources
Semigroup crossed products and Hecke algebras arising from number fields
Documenta Mathematica, 1997 Recently Bost and Connes considered a Hecke C -algebra arising from the ring inclusion of Z in Q, and a C -dynamical system involving this algebra. Laca and Raeburn realized this algebra as a semigroup crossed product, and studied it using techniques ...
Jane Arledge, Marcelo Laca, I. Raeburn
semanticscholar +1 more source
Krein-space operators determined by free product algebras induced by primes and graphs
Special Matrices, 2017 In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
doaj +1 more source
On a principal ideal domain that is not a Euclidean domain
, 2013 The ring Z[ √−19 2 ] is usually given as a first example of a principal ideal domain (PID) that is not a Euclidean domain. This paper gives an elementary and more direct proof that Z[ √−19 2 ] is indeed a PID.
Conan Wong
semanticscholar +1 more source
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
core +1 more source
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
core +1 more source
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
doaj +1 more source
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
core +1 more source
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
doaj +1 more source
On p-rationality of number fields. Applications – PARI/GP programs
, 2019 — LetK be a number field. We prove that its ray class group modulo p2 (resp. 8) if p > 2 (resp. p = 2) characterizes its p-rationality. Then we give two short and very fast PARI Programs (Sections 3.1, 3.2) testing if K (defined by an irreducible monic ...
Georges Gras
semanticscholar +1 more source