Volume function and Mahler measure of exact polynomials
Keyword(s):
We study a class of two-variable polynomials called exact polynomials which contains $A$ -polynomials of knot complements. The Mahler measure of these polynomials can be computed in terms of a volume function defined on the vanishing set of the polynomial. We prove that the local extrema of the volume function are on the two-dimensional torus and give a closed formula for the Mahler measure in terms of these extremal values. This formula shows that the Mahler measure of an irreducible and exact polynomial divided by $\pi$ is greater than the amplitude of the volume function. We also prove a K-theoretic criterion for a polynomial to be a factor of an $A$ -polynomial and give a topological interpretation of its Mahler measure.
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2017 ◽
Vol 39
(3)
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pp. 764-794
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2011 ◽
Vol 75
(5)
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pp. 1007-1045
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2016 ◽
Vol 345
(1)
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pp. 271-304
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1981 ◽
Vol 1981
(328)
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pp. 1-8
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