A formula for the Mahler measure of axy + bx + cy + d

We introduce a formula for the Mahler measure of axy + bx + cy + d with complex coefficients a, b, c, and d and give examples which demonstrate a connection with L-functions. We then prove a generalization of Maillot’s formula when the coefficients are real. Next we discuss operations on the coefficients which fix the Mahler measure. Finally, we prove an alternate formulation of the main result in order to calculate the Mahler measure of a two-parameter family of polynomials in three variables