Year: 2026
Type: preprint
Abstract: We prove Kitaoka's conjecture for all real cyclotomic fields, i.e. for fields of the form $\mathbb{Q}(ζ_k+ζ_k^{-1})$ where $ζ_k$ is a primitive $k$th root of unity. More precisely, we show that such a field admits a universal classical ternary quadratic form if and only if it is a real quadratic field.
Source: arXiv (Cornell University)
Author: Krásenský, Jakub
Institution: Czech Technical University in Prague
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221800942