Odd vanishing cycles in cyclotomic fields
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929676893552640 |
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| author | Hertling, Claus Larabi, Khadija |
| author_facet | Hertling, Claus Larabi, Khadija |
| contents | A cusp of a Hecke group $G_q$ has two natural lifts to the ring of integers of a cyclotomic field. These lifts are called here odd vanishing cycles. All lifts of all cusps together form a discrete subset of ${\mathbb C}$ of some exquisite beauty. They form one or two or four orbits of a certain subgroup of the matrix Hecke group. The subgroup can be considered as a monodromy group and is an analog of a rank 2 Coxeter group, so of a dihedral group. The paper has a research part and a larger survey part. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_08813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Odd vanishing cycles in cyclotomic fields Hertling, Claus Larabi, Khadija Number Theory 11R18, 11R04, 20H25, 20F05, 11B05 A cusp of a Hecke group $G_q$ has two natural lifts to the ring of integers of a cyclotomic field. These lifts are called here odd vanishing cycles. All lifts of all cusps together form a discrete subset of ${\mathbb C}$ of some exquisite beauty. They form one or two or four orbits of a certain subgroup of the matrix Hecke group. The subgroup can be considered as a monodromy group and is an analog of a rank 2 Coxeter group, so of a dihedral group. The paper has a research part and a larger survey part. |
| title | Odd vanishing cycles in cyclotomic fields |
| topic | Number Theory 11R18, 11R04, 20H25, 20F05, 11B05 |
| url | https://arxiv.org/abs/2501.08813 |