Jack Klys
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View article: Densities of eigenspaces of Frobenius and distributions of R-modules
Densities of eigenspaces of Frobenius and distributions of R-modules Open
For any polynomial $p\left(x\right)$ over $\mathbb{F}_{l}$ we determine the asymptotic density of hyperelliptic curves over $\mathbb{F}_{q}$ of genus $g$ for which $p\left(x\right)$ divides the characteristic polynomial of Frobenius acting…
View article: Moments of unramified 2-group extensions of quadratic fields
Moments of unramified 2-group extensions of quadratic fields Open
Let $f\left(K\right)$ be the number of unramified extensions $L/K$ of a quadratic number field $K$ with $\mathrm{Gal}\left(L/K\right)=H$ and $\mathrm{Gal}\left(L/\mathbb{Q}\right)=G$ where $G$ is a central extension of $\mathbb{F}_{2}^{n}$…
View article: Statistics of class groups and related topics
Statistics of class groups and related topics Open
We prove several results concering class groups of number fields and function fields.\nFirstly we compute all the moments of the $p$-torsion in the first step of a filtration of the class group defined by Gerth for cyclic number fields of …
View article: The distribution of $H_{8}$-extensions of quadratic fields
The distribution of $H_{8}$-extensions of quadratic fields Open
We compute all the moments of a normalization of the function which counts unramified $H_{8}$-extensions of quadratic fields, where $H_{8}$ is the quaternion group of order 8, and show that the values of this function determine a constant …