Mahler measure of a linear form in four variables

I review the notion of the Mahler measure of a Laurent polynomial,
state the known results and conjectures on the Mahler
measure of a linear form 1+x_1+...+x_n for n <= 5.
Then I relate the Mahler measure varying in families to Picard-Fuchs
differential equations and modularity (following F.Rodriguez-Villegas).
Finally I give the formula we obtained in a joined work with
M. Vlasenko for a linear form with n=4 which relates this particular
Mahler's measure to a double L-value of two modular
forms with poles.