There is no 290-Theorem for higher degree forms
Number Theory
2025-10-27 v2
Abstract
We study the universality of forms of degrees greater than 2 over rings of integers of totally real number fields. We show that such universal forms always exist, but cannot be characterized by any variant of the 290-Theorem of Bhargava-Hanke.
Keywords
Cite
@article{arxiv.2405.10660,
title = {There is no 290-Theorem for higher degree forms},
author = {Vitezslav Kala and Om Prakash},
journal= {arXiv preprint arXiv:2405.10660},
year = {2025}
}
Comments
12 pages, to appear in Math. Nachr