Limits of Mahler measures in multiple variables
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917916946989056 |
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| author | Brunault, François Guilloux, Antonin Mehrabdollahei, Mahya Pengo, Riccardo |
| author_facet | Brunault, François Guilloux, Antonin Mehrabdollahei, Mahya Pengo, Riccardo |
| contents | We prove that certain sequences of Laurent polynomials, obtained from a fixed Laurent polynomial P by monomial substitutions, give rise to sequences of Mahler measures which converge to the Mahler measure of P. This generalizes previous work of Boyd and Lawton, who considered univariate monomial substitutions. We provide moreover an explicit upper bound for the error term in this convergence, generalizing work of Dimitrov and Habegger, and a full asymptotic expansion for a family of 2-variable polynomials, whose Mahler measures were studied independently by the third author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12259 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Limits of Mahler measures in multiple variables Brunault, François Guilloux, Antonin Mehrabdollahei, Mahya Pengo, Riccardo Number Theory 11R06 We prove that certain sequences of Laurent polynomials, obtained from a fixed Laurent polynomial P by monomial substitutions, give rise to sequences of Mahler measures which converge to the Mahler measure of P. This generalizes previous work of Boyd and Lawton, who considered univariate monomial substitutions. We provide moreover an explicit upper bound for the error term in this convergence, generalizing work of Dimitrov and Habegger, and a full asymptotic expansion for a family of 2-variable polynomials, whose Mahler measures were studied independently by the third author. |
| title | Limits of Mahler measures in multiple variables |
| topic | Number Theory 11R06 |
| url | https://arxiv.org/abs/2203.12259 |