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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.10252 |
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| _version_ | 1866914798996815872 |
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| author | Kotsovolis, Giorgos |
| author_facet | Kotsovolis, Giorgos |
| contents | We show that the spectrum of every $\mathbb{R}-$isotropic homogeneous binary form $P$ of degree $n\geq3$ is an interval of the form $[0,M_P],$ where $M_P$ is some positive constant. This completes the discussion around a conjecture of Mordell from 1940 (disproved by Davenport) regarding the existence of spectral gaps for binary cubic forms and further settles Mahler's program for binary forms of every degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10252 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bass Note Spectra of Binary Forms Kotsovolis, Giorgos Number Theory Dynamical Systems 11H50, 11H16, 11J06 We show that the spectrum of every $\mathbb{R}-$isotropic homogeneous binary form $P$ of degree $n\geq3$ is an interval of the form $[0,M_P],$ where $M_P$ is some positive constant. This completes the discussion around a conjecture of Mordell from 1940 (disproved by Davenport) regarding the existence of spectral gaps for binary cubic forms and further settles Mahler's program for binary forms of every degree. |
| title | Bass Note Spectra of Binary Forms |
| topic | Number Theory Dynamical Systems 11H50, 11H16, 11J06 |
| url | https://arxiv.org/abs/2405.10252 |