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 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 کاملPerron-Frobenius Properties of General Matrices
A matrix is said to have the Perron-Frobenius property if it has a positive dominant eigenvalue that corresponds to a nonnegative eigenvector. Matrices having this and similar properties are studied in this paper. Characterizations of collections of such matrices are given in terms of the spectral projector. Some combinatorial, spectral, and topological properties of such matrices are presented...
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 کاملGeneralized Perron-Frobenius Theorem for Nonsquare Matrices
The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. H...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1992
ISSN: 0022-314X
DOI: 10.1016/0022-314x(92)90040-v