A Natural Series for the Natural Logarithm
Copyright policy )A Natural Series for the Natural Logarithm
Rodriguez Villegas expressed the Mahler measure of a polynomial in terms of an infinite series. Lück's combinatorial $L^2$-torsion leads to similar series expressions for the Gromov norm of a knot complement. In this note we show that those formulae yield interesting power series expansions for the logarithm function. This generalizes an infinite series of Lehmer for the natural logarithm of $4$.
- Louisiana State University United States
volume, knot complement, Mahler measure, Heights, combinatorial \(L^2\)-torsion, Knots and links in the \(3\)-sphere, Gromov norm, Factorials, binomial coefficients, combinatorial functions
volume, knot complement, Mahler measure, Heights, combinatorial \(L^2\)-torsion, Knots and links in the \(3\)-sphere, Gromov norm, Factorials, binomial coefficients, combinatorial functions
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