The Shintani--Faddeev modular cocycle: Stark units from $q$-Pochhammer ratios
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909599313952768 |
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| author | Kopp, Gene S. |
| author_facet | Kopp, Gene S. |
| contents | We give a new interpretation of Stark units associated to real quadratic fields as real multiplication values of a modular cocycle. The cocycle of interest is a meromorphic factor describing the modular transformations of the $q$-Pochhammer symbol and is related to the Shintani--Barnes double sine function and the Faddeev quantum dilogarithm. We prove a refinement of Shintani's Kronecker limit formula that relates square roots of Stark class invariants to real multiplication values of the cocycle, which are cohomological invariants. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_06763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Shintani--Faddeev modular cocycle: Stark units from $q$-Pochhammer ratios Kopp, Gene S. Number Theory 11R37 (Primary), 11F37, 11F67, 11R27, 11R42, 11R54 (Secondary) We give a new interpretation of Stark units associated to real quadratic fields as real multiplication values of a modular cocycle. The cocycle of interest is a meromorphic factor describing the modular transformations of the $q$-Pochhammer symbol and is related to the Shintani--Barnes double sine function and the Faddeev quantum dilogarithm. We prove a refinement of Shintani's Kronecker limit formula that relates square roots of Stark class invariants to real multiplication values of the cocycle, which are cohomological invariants. |
| title | The Shintani--Faddeev modular cocycle: Stark units from $q$-Pochhammer ratios |
| topic | Number Theory 11R37 (Primary), 11F37, 11F67, 11R27, 11R42, 11R54 (Secondary) |
| url | https://arxiv.org/abs/2411.06763 |