Primitively 2-universal senary integral quadratic forms

For a positive integer m , a (positive definite integral) quadratic form is called primitively m-universal if it primitively represents all quadratic forms of rank m . It was proved in [9] that there are exactly 107 equivalence classes of primitively 1-universal quaternary quadratic forms. In this article, we prove that the minimal rank of primitively 2universal quadratic forms is six, and there are exactly 201 equivalence classes of primitively 2-universal senary quadratic forms. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.