On the $p$-divisibility of class numbers of an infinite family of imaginary quadratic fields $\mathbb{Q} (\sqrt{d})$ and $\mathbb{Q} (\sqrt{d+1}).$

Pasupulati Sunil Kumar; Srilakshmi Krishnamoorthy

doi:10.1017/s001708952100015x

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arXiv · 2005.12084

On the $p$-divisibility of class numbers of an infinite family of imaginary quadratic fields $\mathbb{Q} (\sqrt{d})$ and $\mathbb{Q} (\sqrt{d+1}).$

Pasupulati Sunil Kumar·Srilakshmi Krishnamoorthy

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Abstract

For any odd prime $p,$ we construct an infinite family of pairs of imaginary quadratic fields $\mathbb{Q}(\sqrt{d}),\mathbb{Q}(\sqrt{d+1})$ whose class numbers are both divisible by $p.$ One of our theorems settles Iizuka's conjecture for the case $n=1$ and $p >2.$

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Pasupulati Sunil Kumar, Srilakshmi Krishnamoorthy. 2020-05-25. On the $p$-divisibility of class numbers of an infinite family of imaginary quadratic fields $\mathbb{Q} (\sqrt{d})$ and $\mathbb{Q} (\sqrt{d+1}).$. https://doi.org/10.1017/s001708952100015x

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