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

摘要

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 $$n ge 2$$ n ≥ 2 , it will be shown that there are only finitely many similarity classes of positive definite strictly n -regular integral quadratic forms in $$n + 4$$ n + 4 variables. This extends the recent finiteness results for strictly regular quaternary quadratic forms by Earnest et al. (J Number Theory 144: 256–266, 2014).