A note on Shintani's invariants
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910013573824512 |
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| author | Yalkinoglu, Bora |
| author_facet | Yalkinoglu, Bora |
| contents | Shintani's celebrated invariants are conjectured to generate abelian extensions of real quadratic number fields, offering a potential solution to Hilbert's 12th problem in that setting. In this note, we derive new expressions for Shintani's invariants by generalizing an observation of Yamamoto, who showed that these invariants - originally formulated using the double sine function - can be expressed in terms of the q-Pochhammer symbol. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07309 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on Shintani's invariants Yalkinoglu, Bora Number Theory Shintani's celebrated invariants are conjectured to generate abelian extensions of real quadratic number fields, offering a potential solution to Hilbert's 12th problem in that setting. In this note, we derive new expressions for Shintani's invariants by generalizing an observation of Yamamoto, who showed that these invariants - originally formulated using the double sine function - can be expressed in terms of the q-Pochhammer symbol. |
| title | A note on Shintani's invariants |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.07309 |