Article
| Title: | On the class number of the maximal real subfields of a family of cyclotomic fields (English) |
| Author: | Ram, Mahesh Kumar |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 3 |
| Year: | 2023 |
| Pages: | 937-940 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | For any square-free positive integer $m\equiv {10}\pmod {16}$ with $m\geq 26$, we prove that the class number of the real cyclotomic field $\mathbb {Q}(\zeta _{4m}+\zeta _{4m}^{-1})$ is greater than $1$, where $\zeta _{4m}$ is a primitive $4m$th root of unity. (English) |
| Keyword: | maximal real subfield of cyclotomic field |
| Keyword: | real quadratic field |
| Keyword: | class number |
| MSC: | 11R11 |
| MSC: | 11R18 |
| MSC: | 11R29 |
| idZBL: | Zbl 07729546 |
| idMR: | MR4632866 |
| DOI: | 10.21136/CMJ.2023.0364-22 |
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| Date available: | 2023-08-11T14:29:32Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151783 |
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| Reference: | [7] Osada, H.: Note on the class-number of the maximal real subfield of a cyclotomic field.Manuscr. Math. 58 (1987), 215-227. Zbl 0602.12002, MR 884993, 10.1007/BF01169091 |
| Reference: | [8] Takeuchi, H.: On the class-number of the maximal real subfield of a cyclotomic field.Can. J. Math. 33 (1981), 55-58. Zbl 0482.12004, MR 608854, 10.4153/CJM-1981-006-8 |
| Reference: | [9] Yamaguchi, I.: On the class-number of the maximal real subfield of a cyclotomic field.J. Reine Angew. Math. 272 (1975), 217-220. Zbl 0313.12003, MR 366874, 10.1515/crll.1975.272.217 |
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