Quaternionic Mahler measure
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866929264791650304 |
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| author | Wang, Weijia Zhang, Hao |
| author_facet | Wang, Weijia Zhang, Hao |
| contents | We introduce the quaternionic Mahler measure for non-commutative polynomials, extending the classical complex Mahler measure. We establish the existence of quaternionic Mahler measure for slice regular polynomials in one and two variables. We study the quaternionic Mahler measure for real and slice regular polynomials, and consider the associated Lehmer problem. Various formulas of quaternionic Mahler measures are proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02851 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quaternionic Mahler measure Wang, Weijia Zhang, Hao Number Theory Complex Variables We introduce the quaternionic Mahler measure for non-commutative polynomials, extending the classical complex Mahler measure. We establish the existence of quaternionic Mahler measure for slice regular polynomials in one and two variables. We study the quaternionic Mahler measure for real and slice regular polynomials, and consider the associated Lehmer problem. Various formulas of quaternionic Mahler measures are proved. |
| title | Quaternionic Mahler measure |
| topic | Number Theory Complex Variables |
| url | https://arxiv.org/abs/2403.02851 |