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

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Abstract: A Perron number is a real algebraic integer of degree , whose conjugates are , such that . In this paper we compute the smallest Perron numbers of degree 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

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Additional Information

**Qiang Wu**

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

Email:
qiangwu@swu.edu.cn

DOI:
https://doi.org/10.1090/S0025-5718-10-02345-8

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