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$p$-adic Mahler measure and
$\mathbb{Z}$-covers of links
Published online by Cambridge University Press: 29 June 2018
Abstract
Let $p$ be a prime number. We develop a theory of
$p$-adic Mahler measure of polynomials and apply it to the study of
$\mathbb{Z}$-covers of rational homology 3-spheres branched over links. We obtain a
$p$-adic analogue of the asymptotic formula of the torsion homology growth and a balance formula among the leading coefficient of the Alexander polynomial, the
$p$-adic entropy and the Iwasawa
$\unicode[STIX]{x1D707}_{p}$-invariant. We also apply the purely
$p$-adic theory of Besser–Deninger to
$\mathbb{Z}$-covers of links. In addition, we study the entropies of profinite cyclic covers of links. We examine various examples throughout the paper.
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- © Cambridge University Press, 2018
References
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