The smallest Perron numbers

Wu, Qiang

doi:10.1090/S0025-5718-10-02345-8

The smallest Perron numbers
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by Qiang Wu;

Math. Comp. 79 (2010), 2387-2394

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

Published electronically: April 26, 2010

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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 $\mathbb {C}$

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