Mahler Measure and Volumes in Hyperbolic Space
نویسنده
چکیده
The Mahler measure of the polynomials tðx 1Þy ðx 1Þ 2 C1⁄2x; y is essentially the sum of volumes of a certain collection of ideal hyperbolic polyhedra in H, 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 (Mém. Soc. Math. Fr. ðN.S.Þ 80 (2000)), and Vandervelde (J. Number Theory 100 (1) (2003), 184–202). These examples seem to be related to the ones studied by Boyd (Number Theory for the Millennium, AK Peters, Boston, 2002, pp. 127–143), and Boyd and Rodriguez Villegas (in press) for some cases of the A-polynomial of one-cusped manifolds. Mathematics Subject Classifications (2000). 51M25, 11G55, 33E20.
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تاریخ انتشار 2004