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arXiv · 2505.17949

Solving quadratic forms in restricted variables with the circle method

Mieke Wessel·Svenja zur Verth
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Abstract

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.

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Mieke Wessel, Svenja zur Verth. 2025-05-23. Solving quadratic forms in restricted variables with the circle method. https://arxiv.org/abs/2505.17949

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