Abstract:The main result of this paper implies that for every positive integer $d\geqslant 2$ there are at least $(d-3)^2/2$ nonconjugate algebraic numbers which have their Mahler measures lying in the interval $(1,2)$. These algebraic numbers are constructed as roots of certain nonreciprocal quadrinomials.
Keywords: Mahler measure, quadrinomials, irreducibility, nonreciprocal numbers
AMS Subject Classification: 11R06, 11R09