Mahler measure and volumes in hyperbolic space
| dc.creator | Lalin, Matilde | |
| dc.date | 2004-01-02 | |
| dc.date.accessioned | 2026-07-07T05:04:20Z | |
| dc.date.available | 2026-07-07T05:04:20Z | |
| dc.description | 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. | |
| dc.description | 25 pages, 11 figures | |
| dc.identifier | https://arxiv.org/abs/math/0401010 | |
| dc.identifier | http://arxiv.org/abs/math/0401010 | |
| dc.identifier | Geometriae Dedicata 107 (1): 211-234, August 2004 | |
| dc.identifier | doi:10.1007/s10711-004-8123-8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69764 | |
| dc.subject | Metric Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | Number Theory | |
| dc.subject | 51M25; 11G55; 33E20 | |
| dc.title | Mahler measure and volumes in hyperbolic space | |
| dc.type | text |