Lambert $W$-function and Gauss class number one conjecture
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909939773997056 |
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| author | Nikolaev, Igor V. |
| author_facet | Nikolaev, Igor V. |
| contents | We study fixed points of a function arising in a representation theory of the Drinfeld modules by the bounded linear operators on a Hilbert space. We prove that such points correspond to number fields of the class number one. As an application, one gets a solution to the Gauss conjecture for the real quadratic fields of class number one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lambert $W$-function and Gauss class number one conjecture Nikolaev, Igor V. Number Theory Operator Algebras 11M55, 46L85 We study fixed points of a function arising in a representation theory of the Drinfeld modules by the bounded linear operators on a Hilbert space. We prove that such points correspond to number fields of the class number one. As an application, one gets a solution to the Gauss conjecture for the real quadratic fields of class number one. |
| title | Lambert $W$-function and Gauss class number one conjecture |
| topic | Number Theory Operator Algebras 11M55, 46L85 |
| url | https://arxiv.org/abs/2512.02232 |