Mahler Measure and the Vol-Det Conjecture
| Autor: | Champanerkar, Abhijit, Kofman, Ilya, Lalín, Matilde |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | J. London Math. Soc. (2) 99 (2019), 872-900 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/jlms.12200 |
| Popis: | The Vol-Det Conjecture relates the volume and the determinant of a hyperbolic alternating link in $S^3$. We use exact computations of Mahler measures of two-variable polynomials to prove the Vol-Det Conjecture for many infinite families of alternating links. We conjecture a new lower bound for the Mahler measure of certain two-variable polynomials in terms of volumes of hyperbolic regular ideal bipyramids. Associating each polynomial to a toroidal link using the toroidal dimer model, we show that every polynomial which satisfies this conjecture with a strict inequality gives rise to many infinite families of alternating links satisfying the Vol-Det Conjecture. We prove this new conjecture for six toroidal links by rigorously computing the Mahler measures of their two-variable polynomials. Comment: 29 pages. V2: Minor changes, fixed typos, improved exposition |
| Databáze: | arXiv |
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