A (positive definite and non-classic integral) quadratic form is called strongly $s$-regular if it satisfies a strong regularity property on the number of representations of squares of integers. In this article, we prove that for any integer $k \ge 2$, there are only finitely many isometry classes of strongly $s$-regular quadratic forms with rank $k$ if the minimum of the nonzero squares that are represented by them is fixed.

中文翻译：

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对正方形表示具有强正则性的二次型

一个（正定和非经典积分）二次形式被称为强 $s$-regular，如果它满足整数平方表示数量的强正则性。在本文中，我们证明对于任何整数 $k \ge 2$，如果由它们表示的非零平方的最小值，则只有有限多个具有秩 $k$ 的强 $s$-正则二次型等距类是固定的。