Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



The smallest Perron numbers

Author: Qiang Wu
Journal: Math. Comp. 79 (2010), 2387-2394
MSC (2010): Primary 11C08, 11R06, 11Y40
Published electronically: April 26, 2010
MathSciNet review: 2684371
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A Perron number is a real algebraic integer $ \mathbf{\alpha} $ of degree $ d \geq 2$, whose conjugates are $ \mathbf{\alpha} _{i}$, such that $ \mathbf{\alpha} >\max _{2 \leq i \leq d} \vert \mathbf{\alpha} _{i} \vert $. In this paper we compute the smallest Perron numbers of degree $ d \leq 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 auxiliary functions. These functions depend on generalizations of the integer transfinite diameter of some compact sets in $ \mathbb{C}$

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 11C08, 11R06, 11Y40

Retrieve articles in all journals with MSC (2010): 11C08, 11R06, 11Y40

Additional Information

Qiang Wu
Affiliation: Department of Mathematics, Southwest University of China, 2 Tiansheng Road Beibei, 400715 Chongqing, China

Keywords: Algebraic integer, maximal modulus, Perron numbers, explicit auxiliary functions, integer transfinite diameter
Received by editor(s): June 9, 2009
Received by editor(s) in revised form: August 21, 2009
Published electronically: April 26, 2010
Additional Notes: This Project was supported by the Natural Science Foundation of Chongqing grant CSTC no. 2008BB0261
Article copyright: © Copyright 2010 American Mathematical Society