English

Solving quadratic forms in restricted variables with the circle method

Number Theory 2025-05-26 v1

Abstract

Let f(x)f(\mathbf x) be a non-singular quadratic form with sufficiently many mixed terms and tt an integer. For a sequence of weights A\mathcal A we study the number of weighted solutions to f(x)=tf(\mathbf x) = t. In particular, we give conditions on both A\mathcal A and ff such that we can use the circle method to count such solutions of bounded height.

Keywords

Cite

@article{arxiv.2505.17949,
  title  = {Solving quadratic forms in restricted variables with the circle method},
  author = {Mieke Wessel and Svenja zur Verth},
  journal= {arXiv preprint arXiv:2505.17949},
  year   = {2025}
}
R2 v1 2026-07-01T02:33:59.427Z