## Classification of one-class spinor genera for quaternary quadratic forms

### Volume 191 / 2019

Acta Arithmetica 191 (2019), 259-287
MSC: 11E20, 11E12.
DOI: 10.4064/aa180309-19-2
Published online: 23 September 2019

#### Abstract

A quadratic form has a one-class spinor genus if its spinor genus consists of a single equivalence class. We determine that there is, up to equivalence, only one primitive integral positive definite quaternary quadratic form which has a one-class spinor genus but not a one-class genus. In all other cases, such quaternary forms either have a genus and spinor genus which coincide, or the genus splits into multiple spinor genera, which in turn split into multiple equivalence classes.