Classification of one-class spinor genera for quaternary quadratic forms
Number Theory
2019-04-18 v2
Abstract
A quadratic form has a one-class spinor genus if its spinor genus consists of a single equivalence class. In this paper, we determine that there is only one primitive quaternary genus which has a one-class spinor genus but not a one-class genus. In all other cases, the genera of primitive quaternary lattices either have a genus and spinor genus which coincide, or the the genus splits into multiple spinor genera, which in turn split into multiple equivalence classes.
Cite
@article{arxiv.1803.03028,
title = {Classification of one-class spinor genera for quaternary quadratic forms},
author = {A. G. Earnest and Anna Haensch},
journal= {arXiv preprint arXiv:1803.03028},
year = {2019}
}