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Classification of one-class spinor genera for quaternary quadratic forms

Volume 191 / 2019

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


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.


  • A. G. EarnestDepartment of Mathematics
    Southern Illinois University
    Carbondale, IL 62901, U.S.A.
  • Anna HaenschDepartment of Mathematics and Computer Science
    Duquesne University
    Pittsburgh, PA 15282, U.S.A.

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