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Displaying 141 – 155 of 155

The Lehmer constants of an annulus

Artūras Dubickas, Chris J. Smyth (2001)

Journal de théorie des nombres de Bordeaux

Let $M (α)$ be the Mahler measure of an algebraic number $α$ , and $V$ be an open subset of $ℂ$ . Then its Lehmer constant $L (V)$ is inf $M {(α)}^{1 / deg (α)}$ , the infimum being over all non-zero non-cyclotomic $α$ lying with its conjugates outside $V$ . We evaluate $L (V)$ when $V$ is any annulus centered at $0$ . We do the same for a variant of $L (V)$ , which we call the transfinite Lehmer constant $L_{\infty} (V)$ .Also, we prove the converse to Langevin’s Theorem, which states that $L (V) > 1$ if $V$ contains a point of modulus $1$ . We prove the corresponding result for $L_{\infty} (V)$ .

The Lehmer strength bounds for total ramification

John Garza (2009)

Acta Arithmetica

The polylogarithm in the field of two irreducible quintics.

L. Lewin, M. Abouzahra (1986)

Aequationes mathematicae

The R₂ measure for totally positive algebraic integers

V. Flammang (2016)

Colloquium Mathematicae

Let α be a totally positive algebraic integer of degree d, i.e., all of its conjugates $α ₁ = α, . . ., α_{d}$ are positive real numbers. We study the set ₂ of the quantities ${(\prod_{i = 1}^{d} {(1 + α ²_{i})}^{1 / 2})}^{1 / d}$ . We first show that √2 is the smallest point of ₂. Then, we prove that there exists a number l such that ₂ is dense in (l,∞). Finally, using the method of auxiliary functions, we find the six smallest points of ₂ in (√2,l). The polynomials involved in the auxiliary function are found by a recursive algorithm.

Théorèmes d'approximation dans les adèles

Annette Decomps-Guilloux (1965/1966)

Séminaire Dubreil. Algèbre et théorie des nombres

Tilings associated with beta-numeration and substitutions.

Berthé, Valérie, Siegel, Anne (2005)

Integers

Tilings associated with non-Pisot matrices

Maki Furukado, Shunji Ito, E. Arthur Robinson (2006)

Annales de l’institut Fourier

Suppose $A \in G l_{d} (ℤ)$ has a 2-dimensional expanding subspace $E^{u}$ , satisfies a regularity condition, called “good star”, and has $A^{*} \geq 0$ , where $A^{*}$ is an oriented compound of $A$ . A morphism $θ$ of the free group on ${1, 2, \dots, d}$ is called a non-abelianization of $A$ if it has structure matrix $A$ . We show that there is a tiling substitution $Θ$ whose “boundary substitution” $θ = \partial Θ$ is a non-abelianization of $A$ . Such a tiling substitution $Θ$ leads to a self-affine tiling of $E^{u} \sim ℝ^{2}$ with $A_{u} {: = A |}_{E_{u}} \in G L_{2} (ℝ)$ as its expansion. In the last section we find conditions on $A$ so...

Tilings of the Square with Similar Rectangles.

G. Szekeres, M. Laczkovich (1995)

Discrete & computational geometry

Un résultat de Schinzel

G. Höhn, N.-P. Skoruppa (1993)

Journal de théorie des nombres de Bordeaux

Une application des nombres de Pisot à l'algorithme de Jacobi-Perron.

R. Paysant-Le Roux, E. Dubois (1984)

Monatshefte für Mathematik

Une caractérisation de certaines classes d'entiers algébriques généralisant les nombres de Salem

Mohamed Kerada (1995)

Acta Arithmetica

Une caractérisation des nombres de Pisot-Salem des corps $p$ -adiques $Q_{p}$

Jean-Pierre Schreiber (1969)

Mémoires de la Société Mathématique de France

Une nouvelle caractérisation des éléments de Pisot dans l'anneau des adèles de Q

Marthe Grandet-Hugo (1989)

Acta Arithmetica

When the intrinsic algebraic entropy is not really intrinsic

Brendan Goldsmith, Luigi Salce (2015)

Topological Algebra and its Applications

The intrinsic algebraic entropy ent(ɸ) of an endomorphism ɸ of an Abelian group G can be computed using fully inert subgroups of ɸ-invariant sections of G, instead of the whole family of ɸ-inert subgroups. For a class of groups containing the groups of finite rank, aswell as those groupswhich are trajectories of finitely generated subgroups, it is proved that only fully inert subgroups of the group itself are needed to comput ent(ɸ). Examples show how the situation may be quite different outside...

Zur Transzendenz gewisser Reihen.

Peter Bundschuh, Attila Pethö (1987)

Monatshefte für Mathematik

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