Pythagoras numbers for infinite algebraic fields
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918357679210496 |
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| author | Daans, Nicolas Gajović, Stevan Man, Siu Hang Yatsyna, Pavlo |
| author_facet | Daans, Nicolas Gajović, Stevan Man, Siu Hang Yatsyna, Pavlo |
| contents | We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic fields. In contrast, we construct infinite degree totally real algebraic fields whose rings of integers have finite Pythagoras numbers, namely, one, two, three, and at least four. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11222 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pythagoras numbers for infinite algebraic fields Daans, Nicolas Gajović, Stevan Man, Siu Hang Yatsyna, Pavlo Number Theory 11E08, 11E25, 11R18, 11R20, 11R80, 12D15 We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic fields. In contrast, we construct infinite degree totally real algebraic fields whose rings of integers have finite Pythagoras numbers, namely, one, two, three, and at least four. |
| title | Pythagoras numbers for infinite algebraic fields |
| topic | Number Theory 11E08, 11E25, 11R18, 11R20, 11R80, 12D15 |
| url | https://arxiv.org/abs/2502.11222 |