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arXiv · 2501.18941

An asymptotic on the logarithms of the relative class numbers of imaginary abelian number fields of prime conductor and large degree

Stéphane Louboutin
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Abstract

An asymptotic on the logarithms of the relative class numbers of the cyclotomic number fields of prime conductors $p$ is known. Here we give an asymptotic on the logarithms of the relative class numbers of the imaginary abelian number fields of prime conductors $p$ and large degrees $m =(p-1)/d$ with $\phi(d)=o(\log p)$. We also show that this asymptotic does not hold true anymore under the only slightly weaker restriction $\phi(d)=O(\log p)$.

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Stéphane Louboutin. 2025-01-31. An asymptotic on the logarithms of the relative class numbers of imaginary abelian number fields of prime conductor and large degree. https://arxiv.org/abs/2501.18941

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