An integral quadratic form is called strictly $n$-regular if it primitivelyrepresents all quadratic forms in $n$ variables that are primitivelyrepresented by its genus. For any $n \geq 2$, it will be shown that there areonly finitely many similarity classes of positive definite strictly $n$-regularintegral quadratic forms in $n + 4$ variables. This extends the recentfiniteness results for strictly regular quaternary quadratic forms byEarnest-Kim-Meyer (2014).
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机译：如果整数二次形式最初以$ n $变量表示所有二次形式，则该变量最初由其属表示。对于任何$ n \ geq 2 $，将显示出在$ n + 4 $变量中，只有有限的许多正相似的正定严格的$ n $-正则积分二次形式。这扩展了Earnest-Kim-Meyer（2014）对严格规则四次二次型的最近性结果。
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