An infinite family of pairs of distinct quartic Galois CM-fields with the same discriminant and regulator
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911367228817408 |
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| author | Iizuka, Yoshichika Konomi, Yutaka |
| author_facet | Iizuka, Yoshichika Konomi, Yutaka |
| contents | We construct an infinite family of pairs of distinct imaginary biquadratic fields and pairs of distinct imaginary cyclic quartic fields with the same discriminant and regulator. We also construct an infinite family of imaginary biquadratic fields and imaginary cyclic quartic fields with the same regulator. Moreover, we give examples of a pair of distinct imaginary biquadratic fields and a pair of distinct imaginary cyclic quartic fields with the same discriminant, regulator and class number. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_23541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An infinite family of pairs of distinct quartic Galois CM-fields with the same discriminant and regulator Iizuka, Yoshichika Konomi, Yutaka Number Theory 11R16 (Primary) 11R27, 11R29, 11R32 (Secondary) We construct an infinite family of pairs of distinct imaginary biquadratic fields and pairs of distinct imaginary cyclic quartic fields with the same discriminant and regulator. We also construct an infinite family of imaginary biquadratic fields and imaginary cyclic quartic fields with the same regulator. Moreover, we give examples of a pair of distinct imaginary biquadratic fields and a pair of distinct imaginary cyclic quartic fields with the same discriminant, regulator and class number. |
| title | An infinite family of pairs of distinct quartic Galois CM-fields with the same discriminant and regulator |
| topic | Number Theory 11R16 (Primary) 11R27, 11R29, 11R32 (Secondary) |
| url | https://arxiv.org/abs/2506.23541 |