Consecutive pure cubic fields with large class number

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.