The Mahler measure of linear forms as special values of solutions of algebraic differential equations

R. TOLEDANO

Rocky Mountain Journal of Mathematics

Año: 2007

We prove that for n>= 4 there is an analytic function F_n(z) satisfying an algebraic differential equation of degree n+1 such that the logarithmic Mahler measure of the linear form Lf_n=x_1+\cdots + x_n can be essentially computed as the evaluation of  F_n(z) at z=n^{-1}. Weshow that the coefficients of the series representing F_n(z) can be computed recursively using the n-th. symmetric power of a second order linear algebraic differential equation and we  givean estimate on the growth of these coefficients.