A Finiteness theorem for positive definite strictly n-regular quadratic forms

2017/06/13 by Chan, Wai Kiu, Marino, Alicia
#11E12 #11E20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.04160

Abstract

An integral quadratic form is called strictly n-regular if it primitively represents all quadratic forms in n variables that are primitively represented by its genus. For any n ≥ 2, it will be shown that there are only finitely many similarity classes of positive definite strictly n-regular integral quadratic forms in n + 4 variables. This extends the recent finiteness results for strictly regular quaternary quadratic forms by Earnest-Kim-Meyer (2014).

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