K. Holm

activity

20202026

collaborators

6 papers

quant-ph2026

Lattice moments and quantum designs

Jonathan Conrad, Kristian Holm

We show that the ensemble of unimodular Gottesman $-$ Kitaev $-$ Preskill distributions fails to form a rigged quantum $3$ -design and quantify the replica defect that determines this f…

math.NT2026

Explicit second moments of symplectic Siegel transforms

Kristian Holm, Seungki Kim

We give two alternate formulations for the second moment formula of the Siegel transform over $Sp (2 n, Z) \ Sp (2 n, R)$ , previously establis…

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…

Lattice moments and quantum designs

Explicit second moments of symplectic Siegel transforms

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 $1$