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Distribution of genus numbers of abelian number fields

Christopher Frei,Daniel Loughran,Rachel Newton

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES（2023）

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Abstract
We study the quantitative behaviour of genus numbers of abelian extensions of number fields with given Galois group. We prove an asymptotic formula for the average value of the genus number and show that any given genus number appears only 0% of the time.
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genus numbers
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