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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2410.03242 |
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| _version_ | 1866918164328087552 |
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| author | Kim, Dohyeong Song, Seungho |
| author_facet | Kim, Dohyeong Song, Seungho |
| contents | The conjecture due to Bertrand and Rodriguez Villegas asserts that the 1-norm of the nonzero element in an exterior power of the units of a number field has a certain lower bound. For the exterior square case of totally real quartic extensions of the rationals, Costa and Friedman gave a lower bound of 0.802. We prove that the bound can be improved to 1.134 when the extension is further assumed to be Galois. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bertrand's and Rodriguez Villegas' Conjecture for real quartic Galois extensions of the rationals Kim, Dohyeong Song, Seungho Number Theory 11R16, 11G50 The conjecture due to Bertrand and Rodriguez Villegas asserts that the 1-norm of the nonzero element in an exterior power of the units of a number field has a certain lower bound. For the exterior square case of totally real quartic extensions of the rationals, Costa and Friedman gave a lower bound of 0.802. We prove that the bound can be improved to 1.134 when the extension is further assumed to be Galois. |
| title | Bertrand's and Rodriguez Villegas' Conjecture for real quartic Galois extensions of the rationals |
| topic | Number Theory 11R16, 11G50 |
| url | https://arxiv.org/abs/2410.03242 |