منابع مشابه
The smallest Perron numbers
A Perron number is a real algebraic integer α of degree d ≥ 2, whose conjugates are αi, such that α > max2≤i≤d |αi|. In this paper we compute the smallest Perron numbers of degree d ≤ 24 and verify that they all satisfy the Lind-Boyd conjecture. Moreover, the smallest Perron numbers of degree 17 and 23 give the smallest house for these degrees. The computations use a family of explicit auxiliar...
متن کاملCounting Perron Numbers by Absolute Value
We count various classes of algebraic integers of fixed degree by their largest absolute value. The classes of integers considered include all algebraic integers, Perron numbers, totally real integers, and totally complex integers. We give qualitative and quantitative results concerning the distribution of Perron numbers, answering in part a question of W. Thurston [Thu].
متن کاملAlgebraic Properties of Weak Perron Numbers
We study algebraic properties of real positive algebraic numbers which are not less than the moduli of their conjugates. In particular, we are interested in the relation of these numbers to Perron numbers.
متن کاملOn the dichotomy of Perron numbers and beta-conjugates
Let β > 1 be an algebraic number. A general definition of a beta-conjugate of β is proposed with respect to the analytical function fβ(z) = −1 + ∑ i≥1 tiz i associated with the Rényi β-expansion dβ(1) = 0.t1t2 . . . of unity. From Szegö’s Theorem, we study the dichotomy problem for fβ(z), in particular for β a Perron number: whether it is a rational fraction or admits the unit circle as natural...
متن کاملTranscendental numbers having explicit g-adic and Jacobi-Perron expansions
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2010
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-10-02345-8