Distribution of genus numbers of abelian number fields
Rachel Newton
King's College London
https://www.kcl.ac.uk/people/dr-rachel-newton
Date(s) : 03/11/2022 iCal
12h00 - 13h00
Let K be a number field and let L/K be an abelian extension. The genus field of L/K is the largest extension of L which is unramified at all places of L and abelian as an extension of K. The genus group is its Galois group over L, which is a quotient of the class group of L, and the genus number is the size of the genus group. We study the quantitative behaviour of genus numbers as one varies over abelian extensions L/K with fixed Galois group. We give an asymptotic formula for the average value of the genus number and show that any given genus number appears only 0% of the time. This is joint work with Christopher Frei and Daniel Loughran.
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