Failures of integral Springer's Theorem
Number Theory
2025-04-17 v2
Abstract
We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove that this phenomenon happens infinitely often, and, conversely, establish finiteness results about the situation when the quadratic form is fixed.
Keywords
Cite
@article{arxiv.2404.12844,
title = {Failures of integral Springer's Theorem},
author = {Nicolas Daans and Vítězslav Kala and Jakub Krásenský and Pavlo Yatsyna},
journal= {arXiv preprint arXiv:2404.12844},
year = {2025}
}
Comments
10 pages, author accepted manuscript