K. Holm

activity

20202026

collaborators

Showing math.NTShow all

4 papers · 1 filter

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.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…

Explicit second moments of symplectic Siegel transforms

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 $1$