Kitaoka's Conjecture and sums of squares
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909864037449728 |
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| author | Kala, Vitezslav Kramer, Kristyna Krasensky, Jakub |
| author_facet | Kala, Vitezslav Kramer, Kristyna Krasensky, Jakub |
| contents | We connect the existence of a ternary classical universal quadratic form over a totally real number field $K$ with the property that all totally positive multiples of 2 are sums of squares (if $K$ does not contain $\sqrt 2$ or contains a nonsquare totally positive unit). In particular, we get that Kitaoka's Conjecture holds for all fields of odd discriminant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kitaoka's Conjecture and sums of squares Kala, Vitezslav Kramer, Kristyna Krasensky, Jakub Number Theory We connect the existence of a ternary classical universal quadratic form over a totally real number field $K$ with the property that all totally positive multiples of 2 are sums of squares (if $K$ does not contain $\sqrt 2$ or contains a nonsquare totally positive unit). In particular, we get that Kitaoka's Conjecture holds for all fields of odd discriminant. |
| title | Kitaoka's Conjecture and sums of squares |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.19545 |