Mahler measure and volumes in hyperbolic space

Details Mahler measure and volumes in hyperbolic space Mahler measure and volumes in hyperbolic space

2004-01-02

arxiv.org/abs/math/0401010v1

Geometriae Dedicata 107 (1): 211-234, August 2004

Mathematics

Metric Geometry

25 pages, 11 figures

Scientific paper

10.1007/s10711-004-8123-8

The Mahler measure of the polynomials $t(x^m-1) y - (x^n-1) \in \dC[x,y]$ is essentially the sum of volumes of a certain collection of ideal hyperbolic polyhedra in $\HH^3$, 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 \cite{M} and Vandervelde \cite{V}. These examples seem to be related to the ones studied by Boyd \cite{B1}, \cite{B2} and Boyd and Rodriguez Villegas \cite{BRV2} for some cases of the $A$-polynomial of one-cusped manifolds.

Affiliated with

Also associated with

No associations

Rating

Mahler measure and volumes in hyperbolic space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mahler measure and volumes in hyperbolic space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mahler measure and volumes in hyperbolic space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-119811