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Primitively 2-universal senary integral quadratic forms

2023/09/03 by Oh, Byeong-Kweon, Yoon, Jongheun
#11E12 #11E20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.01061

Abstract

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 arXiv:2202.13573 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 2-universal quadratic forms is six, and there are exactly 201 equivalence classes of primitively 2-universal senary quadratic forms.

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