Solving quadratic forms in restricted variables with the circle method

2025/05/23 by Wessel, Mieke, Verth, Svenja zur
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.17949

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.

Citations

• A minimalist version of the circle method and Diophantine problems over thin sets
• The quadratic form in 9 prime variables

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• Quantitative strong approximation for ternary quadratic forms I