Additively indecomposable quadratic forms over biquadratic and simplest cubic fields
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908821589327872 |
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| author | Fryšová, Simona Tinková, Magdaléna |
| author_facet | Fryšová, Simona Tinková, Magdaléna |
| contents | In this paper, we study additively indecomposable quadratic forms over real biquadratic and simplest cubic fields. In particular, we show that over these fields, we can always find such a classical form in 2 variables, which differs from the situation for forms over integers. Moreover, for some cases, we derive a lower bound on the number of classical, additively indecomposable binary quadratic forms up to equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Additively indecomposable quadratic forms over biquadratic and simplest cubic fields Fryšová, Simona Tinková, Magdaléna Number Theory In this paper, we study additively indecomposable quadratic forms over real biquadratic and simplest cubic fields. In particular, we show that over these fields, we can always find such a classical form in 2 variables, which differs from the situation for forms over integers. Moreover, for some cases, we derive a lower bound on the number of classical, additively indecomposable binary quadratic forms up to equivalence. |
| title | Additively indecomposable quadratic forms over biquadratic and simplest cubic fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.23857 |