Kitaoka's Conjecture for quadratic fields
Number Theory
2025-02-03 v1
Abstract
We prove that there are at most 13 real quadratic fields that admit a ternary universal quadratic lattice, thus establishing a strong version of Kitaoka's Conjecture for quadratic fields. More generally, we obtain explicit upper bounds on the discriminants of real quadratic fields with a quadratic lattice of rank at most 7 that represents all totally positive multiples of a fixed integer.
Cite
@article{arxiv.2501.19371,
title = {Kitaoka's Conjecture for quadratic fields},
author = {Vitezslav Kala and Jakub Krásenský and Dayoon Park and Pavlo Yatsyna and Błażej Żmija},
journal= {arXiv preprint arXiv:2501.19371},
year = {2025}
}
Comments
27 pages; comments are welcome!