Estimates for mahler's measure of a linear form - Rodriguez Villegas, Fernando (2004)
Let La(z) = a1z1+a2z2 + ... + aNzN be a linear form in N complex variables z1,z2,...,zN with non-zero coefficients. We establish several estimates for the logarithmic Mahler measure of La. In general, we show that the logarithmic Mahler measure of La(x) and the logarithm of the norm of a differ by a bounded amount that is independent of N. We prove a further estimate which is useful for making an approximate numerical evaluation of the logarithmic Mahler measure.