K. Holm

activity

20202024

collaborators

4 papers

math.GR2024

The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group

Amir Džambić, Kristian Holm, Ralf Köhl

Let $n ⩾ 2$ . We prove that, up to conjugation, $Sp_{2 n} (Z)$ is the unique lattice in $Sp_{2 n} (R)$ of the smallest covolume.

math.NT2023

The $1$ -Level Density for Zeros of Hecke $L$ -Functions of Imaginary Quadratic Number Fields of Class Number $1$

Kristian Holm

Let $K = Q (- d)$ be an imaginary quadratic number field of class number $1$ and $O_{K}$ its ring of integers. We study a family of Hecke…

math.NT2022

A Central Limit Theorem for Counting Functions Related to Symplectic Lattices and Bounded Sets

Kristian Holm

We use a method developed by Björklund and Gorodnik to show a central limit theorem (as $T$ tends to $\infty$ ) for the counting functions $# (Λ \cap Ω_{T})$ where $Λ$ ra…

math.NT2020

On The Distribution Of Angles Between Increasingly Many Short Lattice Vectors

Kristian Holm

Following Södergren, we consider a collection of random variables on the space $X_{n}$ of unimodular lattices in dimension $n$ : Normalizations of the angles between the $N = N (n)$ sh…

The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group

The 1-Level Density for Zeros of Hecke L-Functions of Imaginary Quadratic Number Fields of Class Number 1

A Central Limit Theorem for Counting Functions Related to Symplectic Lattices and Bounded Sets

On The Distribution Of Angles Between Increasingly Many Short Lattice Vectors

The $1$ -Level Density for Zeros of Hecke $L$ -Functions of Imaginary Quadratic Number Fields of Class Number $1$