On the measure of a nonreciprocal algebraic number (Q1840494)

For an algebraic number \(\alpha\) let \(M(\alpha)\) be its Mahler measure and let \(G(\alpha)\) be the absolute value of the product of logarithms of absolute values of all conjugates of \(\alpha\). It is shown that if \(\alpha\) is irrational and nonreciprocal then \(M(\alpha)^2G(\alpha)(1/d)\geq 1/2d\), with \(d\) being the degree of \(\alpha\).