For a given positive integer $k$, we prove that there are at least $x^{1/2-o(1)}$ integers $d\leq x$ such that the real quadratic fields ${\mathbb {Q}}(\sqrt {d+1}),\dots ,{\mathbb {Q}}(\sqrt {d+k})$ have class numbers essentially as large as possible.

中文翻译：

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具有大类数的连续实二次域

对于给定的正整数 $k$，我们证明至少有 $x^{1/2-o(1)}$ 个整数 $d\leq x$ 使得实二次域 ${\mathbb {Q} }(\sqrt {d+1}),\dots ,{\mathbb {Q}}(\sqrt {d+k})$ 具有尽可能大的类号。