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Salem numbers as Mahler measures of Gaussian Pisot numbers

Volume 194 / 2020

Toufik Zaïmi Acta Arithmetica 194 (2020), 383-392 MSC: Primary 11R06; Secondary 11R80, 11J7. DOI: 10.4064/aa181208-14-7 Published online: 28 March 2020

Abstract

A Gaussian Pisot number is an algebraic integer with modulus greater than 1 whose other conjugates, over the quadratic field $\mathbb {Q}(\sqrt {-1}),$ are of modulus less than 1. We determine all nonreciprocal Gaussian Pisot numbers whose Mahler measures are Salem numbers.

Authors

  • Toufik ZaïmiDepartment of Mathematics and Statistics
    College of Science
    Imam Mohammad Ibn Saud Islamic University (IMSIU)
    P.O. Box 90950
    Riyadh 11623, Saudi Arabia
    e-mail

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