Title:
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Asymptotics of Twisted Alexander Polynomials and Hyperbolic Volume
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Author:
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Bénard, L.; Dubois, J.; Heusener, M.; Porti, J.
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Abstract:
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For a hyperbolic knot and a natural number n, we consider the Alexander polynomial twisted by the n-th symmetric power of a lift of the holonomy. We establish the asymptotic behavior of these twisted Alexander polynomials evaluated at unit complex numbers, yielding the volume of the knot exterior. More generally, we prove this asymptotic behavior for cusped hyperbolic manifolds of finite volume. The proof relies on results of Müller, and Menal-Ferrer and the last author. Using the uniformity of the convergence, we also deduce a similar asymptotic result for the Mahler measures of those polynomials. © 2022 Department of Mathematics, Indiana University. All rights reserved. |
Publication date:
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2022-01-01 |
Subject(s):
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Alexander Polynomials, Hypervolic Volume, Mathematics |
Rights:
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L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/ |
Pages:
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46 p. |
Document type:
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Article Article - Accepted version |
DOI:
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10.1512/iumj.2022.71.8937
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Published by:
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Department of Mathematics, Indiana University
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