A Class of Discrete Spectra of Non-Pisot Numbers
A note on linear recurrent Mahler numbers.
A self-similar tiling generated by the minimal Pisot number
Abstract -expansions and ultimately periodic representations
For abstract numeration systems built on exponential regular languages (including those coming from substitutions), we show that the set of real numbers having an ultimately periodic representation is if the dominating eigenvalue of the automaton accepting the language is a Pisot number. Moreover, if is neither a Pisot nor a Salem number, then there exist points in which do not have any ultimately periodic representation.
Adèles et séries trigonométriques spéciales
Algebraic numbers near the unit circle
Algébricité des fonctions méromorphes prenant certaines valeurs algébriques
Algorithme de Jacobi-Perron dans les corps de nombres de degré 4
An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation
An effective lower bound for the height of algebraic numbers
An extension of a result of C. J. Smyth to polynomials in several variables
Applications de la notion d'entropie au développement d'un nombre réel dans une base de Pisot
Soit un nombre de Pisot de degré ; nous avons montré précédemment que l’endomorphisme du tore dont est valeur propre est facteur du -shift bilatéral par une application continue ; nous prouvons ici (théorème 1) que l’application conserve l’entropie de toute mesure invariante sur le -shift. Ceci permet de définir l’entropie d’un nombre dans la base et d’en étudier la stabilité. Nous généralisons également des résultats de Kamae, Rauzy et Bernay.
Arithmetic groups and salem numbers.
Arithmetics in numeration systems with negative quadratic base
We consider positional numeration system with negative base , as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when is a quadratic Pisot number. We study a class of roots of polynomials , , and show that in this case the set of finite -expansions is closed under addition, although it is not closed under subtraction. A particular example is , the golden ratio. For such , we determine the exact bound on the number of fractional digits...
Arithmetics of beta-expansions
Asymptotic nature of higher Mahler measure
We consider Akatsuka’s zeta Mahler measure as a generating function of the higher Mahler measure of a polynomial where is the integral of over the complex unit circle. Restricting ourselves to P(x) = x - r with |r| = 1 we show some new asymptotic results regarding , in particular as k → ∞.