Mahler measure and volumes in hyperbolic space

الأصل · EN

The Mahler measure of the polynomials t(xᵐ-1) y - (xⁿ-1) ∈ [x,y] is essentially the sum of volumes of a certain collection of ideal hyperbolic polyhedra in ³, which can be determined a priori as a function on the parameter t. We obtain a formula that generalizes some previous formulas given by Cassaigne and Maillot M and Vandervelde V. These examples seem to be related to the ones studied by Boyd B1, B2 and Boyd and Rodriguez Villegas BRV2 for some cases of the A-polynomial of one-cusped manifolds.