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arXiv · 2111.11549

Consecutive real quadratic fields with large class numbers

Giacomo Cherubini·Alessandro Fazzari·Andrew Granville·Vítězslav Kala·Pavlo Yatsyna
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Abstract

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.

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Giacomo Cherubini, Alessandro Fazzari, Andrew Granville, Vítězslav Kala, Pavlo Yatsyna. 2021-11-22. Consecutive real quadratic fields with large class numbers. https://doi.org/10.1093/imrn%2Frnac176

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