Solving quadratic forms in restricted variables with the circle method
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916754844811264 |
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| author | Wessel, Mieke Verth, Svenja zur |
| author_facet | Wessel, Mieke Verth, Svenja zur |
| contents | Let $f(\mathbf x)$ be a non-singular quadratic form with sufficiently many mixed terms and $t$ an integer. For a sequence of weights $\mathcal A$ we study the number of weighted solutions to $f(\mathbf x) = t$. In particular, we give conditions on both $\mathcal A$ and $f$ such that we can use the circle method to count such solutions of bounded height. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving quadratic forms in restricted variables with the circle method Wessel, Mieke Verth, Svenja zur Number Theory Let $f(\mathbf x)$ be a non-singular quadratic form with sufficiently many mixed terms and $t$ an integer. For a sequence of weights $\mathcal A$ we study the number of weighted solutions to $f(\mathbf x) = t$. In particular, we give conditions on both $\mathcal A$ and $f$ such that we can use the circle method to count such solutions of bounded height. |
| title | Solving quadratic forms in restricted variables with the circle method |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.17949 |