No proper generalized quadratic forms are universal over quadratic fields
Number Theory
2024-09-13 v1
Abstract
We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be universal if it contains a quadratic subform that is universal. We also construct an example illustrating that the positive-definiteness condition is necessary.
Keywords
Cite
@article{arxiv.2409.07941,
title = {No proper generalized quadratic forms are universal over quadratic fields},
author = {Ondřej Chwiedziuk and Matěj Doležálek and Simona Hlavinková and Emma Pěchoučková and Zdeněk Pezlar and Om Prakash and Anna Růžičková and Mikuláš Zindulka},
journal= {arXiv preprint arXiv:2409.07941},
year = {2024}
}