A proof of Sugawara's conjecture on Hasse-Weber ray class invariants
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909533160341504 |
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| author | Morton, Patrick |
| author_facet | Morton, Patrick |
| contents | In this paper a proof is given of Sugawara's conjecture from 1936, that the ray class field of conductor $\mathfrak{f}$ over an imaginary quadratic field $K$ is generated over $K$ by a single primitive $\mathfrak{f}$-division value of the $τ$-function, first defined by Weber and then modified by Hasse in his 1927 paper giving a new foundation of complex multiplication. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A proof of Sugawara's conjecture on Hasse-Weber ray class invariants Morton, Patrick Number Theory In this paper a proof is given of Sugawara's conjecture from 1936, that the ray class field of conductor $\mathfrak{f}$ over an imaginary quadratic field $K$ is generated over $K$ by a single primitive $\mathfrak{f}$-division value of the $τ$-function, first defined by Weber and then modified by Hasse in his 1927 paper giving a new foundation of complex multiplication. |
| title | A proof of Sugawara's conjecture on Hasse-Weber ray class invariants |
| topic | Number Theory |
| url | https://arxiv.org/abs/2406.11479 |