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arXiv · 1803.03028

Classification of one-class spinor genera for quaternary quadratic forms

A. G. Earnest·Anna Haensch
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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.

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A. G. Earnest, Anna Haensch. 2018-03-08. Classification of one-class spinor genera for quaternary quadratic forms. https://arxiv.org/abs/1803.03028

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