Abstract
Suppose that an algebraic number β of degree d = n(n − 1) over ℚ is expressible by the difference of two conjugate algebraic integers α1 ≠ α2 of degree n, namely, β = α1− α2. We prove that then there exists a constant c > 1, which depends on \( \overline{\mid \alpha \mid } \) = max1≤i≤n ∣αi∣ only, such that M(β)1/d > c.
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Dedicated to Professors Antanas Laurinčikas and Eugenijus Manstavičius on the occasion of their 70th birthdays
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* This research was funded by the European Social Fund according to the activity “Improvement of researchers” qualification by implementing world-class R&D projects’ of Measure No. 09.3.3-LMT-K-712-01-0037.
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Dubickas, A. Mahler measure of a difference of two conjugates*. Lith Math J 59, 48–53 (2019). https://doi.org/10.1007/s10986-019-09424-1
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DOI: https://doi.org/10.1007/s10986-019-09424-1