arXiv subjects

Annalena Wernz

Publications and source records attributed to Annalena Wernz.

3 recordsLinked to original sources

arXiv2021

The maximal discrete extension of the Hermitian modular group

Let $Γ_n(\mathcal{\scriptstyle{O}}_\mathbb{K})$ denote the Hermitian modular group of degree $n$ over an imaginary-quadratic number field $\mathbb{K}$. In this paper we determine its maximal discrete extension in $SU(n,n;\mathbb{C})$, which coincides with the normalizer of $Γ_n(\mathcal{\scriptstyle{O}}_{\mathbb{K}})$. The description involves the $n$-torsion subgroup of the ideal class group of $\mathbb{K}$. This group is defined over a particular number field $\widehat{\mathbb{K}}_n$ and we can describe the ramified primes in it. In the case $n=2$ we give an explicit description, which involves generalized Atkin-Lehner involutions. Moreover we find a natural characterization of this group in $SO(2,4)$.

math.NT↗

arXiv2020

Hermitian theta series and Maaß spaces under the action of the maximal discrete extension of the Hermitian modular group

Let $Γ_n(\mathcal{\scriptstyle{O}}_{\mathbb{K}})$ denote the Hermitian modular group of degree $n$ over an imaginary quadratic number field $\mathbb{K}$ and $Δ_{n,\mathbb{K}}^*$ its maximal discrete extension in the special unitary group $SU(n,n;\mathbb{C})$. In this paper we study the action of $Δ_{n,\mathbb{K}}^*$ on Hermitian theta series and Maass spaces. For $n=2$ we will find theta lattices such that the corresponding theta series are modular forms with respect to $Δ_{2,\mathbb{K}}^*$ as well as examples where this is not the case. Our second focus lies on studying two different Maass spaces. We will see that the new found group $Δ_{2,\mathbb{K}}^*$ consolidates the different definitions of the spaces.

math.NT↗

arXiv2019

The maximal discrete extension of $SL_2(\mathcal{\scriptstyle{O}}_K)$ for an imaginary-quadratic number field $K$

Let $\mathcal{\scriptstyle{O}}_K$ be the ring of integers of an imaginary quadratic number field $K$. In this paper we give a new description of the maximal discrete extension of the group $SL_2(\mathcal{\scriptstyle{O}}_K)$ inside $SL_2(\mathbb{C})$, which uses generalized Atkin-Lehner involutions. Moreover we find a natural characterization of this group in $SO(1,3)$.

math.NT↗