Class number zeta function of imaginary quadratic fields
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914421117288448 |
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| author | Nikolaev, Igor V. |
| author_facet | Nikolaev, Igor V. |
| contents | We introduce a zeta function counting imaginary quadratic number fields by their class numbers. It is proved that such a function is rational depending only on the eight roots of unity of degrees $1$ and $2$. As a corollary, one gets a lower bound $2p$ for the number of imaginary quadratic fields of the prime class number $p$. Our method is based on the study of periodic points of a dynamical system arising in the representation theory of the Drinfeld modules by the bounded linear operators on a Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24313 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Class number zeta function of imaginary quadratic fields Nikolaev, Igor V. Number Theory Dynamical Systems Operator Algebras 11M55, 46L85 We introduce a zeta function counting imaginary quadratic number fields by their class numbers. It is proved that such a function is rational depending only on the eight roots of unity of degrees $1$ and $2$. As a corollary, one gets a lower bound $2p$ for the number of imaginary quadratic fields of the prime class number $p$. Our method is based on the study of periodic points of a dynamical system arising in the representation theory of the Drinfeld modules by the bounded linear operators on a Hilbert space. |
| title | Class number zeta function of imaginary quadratic fields |
| topic | Number Theory Dynamical Systems Operator Algebras 11M55, 46L85 |
| url | https://arxiv.org/abs/2603.24313 |