On the Mahler measure of the composition of two polynomials
The integer transfinite diameter of intervals and totally real algebraic integers
In this paper we build on some recent work of Amoroso, and Borwein and Erdélyi to derive upper and lower estimates for the integer transfinite diameter of small intervals , where is a fixed rational and . We also study functions associated with transfinite diameters of Farey intervals. Then we consider certain polynomials, which we call polynomials, associated to a given interval . We show how to estimate from below the proportion of roots of an integer polynomial which is sufficiently small...
New methods providing high degree polynomials with small Mahler measure.
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