Consecutive pure cubic fields with large class number

Dongho Byeon, Donggeon Yhee
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Abstract

In this paper, we prove that for a given positive integer k, there are at least \(x^{1/3-o(1)}\) integers \(d \le x\) such that the consecutive pure cubic fields \({\mathbb {Q}}(\root 3 \of {d+1})\), \(\cdots \), \({\mathbb {Q}}(\root 3 \of {d+k})\) have arbitrarily large class numbers.

大类数连续纯立方场
在本文中,我们证明了对于给定的正整数 k,至少有 \(x^{1/3-o(1)}\) 个整数 \(d \le x\) 使得连续的纯立方域 \({\mathbb {Q}}(\root 3 \of {d+1})\)、\(cdots), ({\mathbb {Q}}(\root 3\of {d+k}))有任意大的类数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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