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Peer-reviewedCC BY 4.0Monatshefte Fur Mathematik

Solving quadratic forms in restricted variables with the circle method

  • Mieke Wessel1
  • Svenja zur Verth2
  1. 1Inria Saclay, 1 Rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
  2. 2École Polytechnique Fédérale de Lausanne/MATH/TAN, Station 8, CH-1015 Lausanne, Switzerland
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Abstract

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}f(x)\end{document}f(x) be a non-singular quadratic form with sufficiently many mixed terms and t an integer. For a sequence of weights \mathcal AA we study the number of weighted solutions to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}f(x) = t\end{document}f(x)=t. In particular, we give conditions on both \mathcal AA and f such that we can use the circle method to count such solutions of bounded height.

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Cite

BibTeXRIS
BibTeX
@article{wessel2026solving,
  title = {{Solving quadratic forms in restricted variables with the circle method}},
  author = {Mieke Wessel and Svenja zur Verth},
  journal = {Monatshefte Fur Mathematik},
  year = {2026},
  month = sep,
  doi = {10.1007/s00605-026-02189-z},
  url = {https://doi.org/10.1007/s00605-026-02189-z},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Solving quadratic forms in restricted variables with the circle method
AU  - Mieke Wessel
AU  - Svenja zur Verth
PY  - 2026
DA  - 2026/09/09
JO  - Monatshefte Fur Mathematik
DO  - 10.1007/s00605-026-02189-z
UR  - https://doi.org/10.1007/s00605-026-02189-z
AB  - Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}f(x)\end{document}f(x) be a non-singular quadratic form with sufficiently many mixed terms and t an integer. For a sequence of weights \mathcal AA we study the number of weighted solutions to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}f(x) = t\end{document}f(x)=t. In particular, we give conditions on both \mathcal AA and f such that we can use the circle method to count such solutions of bounded height.
SN  - 0026-9255
SN  - 1436-5081
ER  -