Finite-Dimensional Mahler Measure of a Polynomial and Szegöʹs Theorem Original Research Article

This paper is concerned with the study of Mahlerʹs measure of an univariate polynomial. A theorem of Szegö says that the measure ofPis equal to the infimum of double vertical barPQdouble vertical bar2whereQis a monic polynomial. Here we study how the infimum of double vertical barPQdouble vertical bar2, whereQis monic and has degreek, tends to the measure ofPwhenktends to infinity: this answers a question raised by Cerlienco, Mignotte and Piras [J. Symbolic Comput.4, No. 1 (1987), 21–34].