Explanipedia

Period functions for vector-valued Maass cusp forms of real weight, with an application to Jacobi Maass cusp forms Open

Anke Pohl, YoungJu Choie, Roelof W. Bruggeman · 2024

For vector-valued Maass cusp forms for~$SL_2(\mathbb{Z})$ with real weight~$k\in\mathbb{R}$ and spectral parameter $s\in\mathbb{C}$, $\mathrm{Re} s\in (0,1)$, $s\not\equiv \pm k/2$ mod $1$, we propose a notion of vector-valued period funct…

Equidistribution of cusp points of Hecke triangle groups Open

Laura Breitkopf, Marc Keßeböhmer, Anke Pohl · 2024

In the framework of infinite ergodic theory, we derive equidistribution results for suitable weighted sequences of cusp points of Hecke triangle groups encoded by group elements of constant word length with respect to a set of natural gene…

Scattering theory with unitary twists Open

Moritz Doll, Ksenia Fedosova, Anke Pohl · 2023

We study the spectral properties of the Laplace operator associated to a hyperbolic surface in the presence of a unitary representation of the fundamental group. Following the approach by Guillopé and Zworski, we establish a factorization …

Fourier expansions of vector-valued automorphic functions with non-unitary twists Open

Ksenia Fedosova, Anke Pohl, Julie Rowlett · 2023

We provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian that are twist-periodic in a horocycle direction. The twist may be given by any endomorphism of a finite-dimensional vector space; no assumptions on …

StuKon<sup>22</sup> – bewährte Veranstaltung in neuem Gewand Open

J. Lehnert, Anke Pohl · 2022

Selberg zeta functions, cuspidal accelerations, and existence of strict transfer operator approaches Open

Anke Pohl, Paul Wabnitz · 2022

For geometrically finite non-compact developable hyperbolic orbisurfaces (including those of infinite volume), we provide transfer operator families whose Fredholm determinants are identical to the Selberg zeta function. Our proof yields a…

Scattering Theory with Unitary Twists Open

Moritz Doll, Ksenia Fedosova, Anke Pohl · 2022

We study the spectral properties of the Laplace operator associated to a hyperbolic surface in the presence of a unitary representation of the fundamental group. Following the approach by Guillopé and Zworski, we establish a factorization …

Fourier expansions of vector-valued automorphic functions with non-unitary twists Open

Ksenia Fedosova, Anke Pohl, Julie Rowlett · 2022

We provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian that are twist-periodic in a horocycle direction. The twist may be given by any endomorphism of a finite-dimensional vector space; no assumptions on …

Counting Resonances on Hyperbolic Surfaces with Unitary Twists Open

Moritz Doll, Ksenia Fedosova, Anke Pohl · 2021

We present the Laplace operator associated to a hyperbolic surface $Γ\setminus\mathbb{H}$ and a unitary representation of the fundamental group $Γ$, extending the previous definition for hyperbolic surfaces of finite area to those of infin…

Symbolic dynamics and transfer operators for Weyl chamber flows: a class of examples Open

Anke Pohl · 2020

We provide special cross sections for the Weyl chamber flow on a sample class of Riemannian locally symmetric spaces of higher rank, namely the direct product spaces of Schottky surfaces. We further present multi-parameter transfer operato…

Density of resonances for covers of Schottky surfaces Open

Anke Pohl, Louis Soares · 2020

We investigate how bounds of resonance counting functions for Schottky surfaces behave under transitions to covering surfaces of finite degree. We consider the classical resonance counting function asking for the number of resonances in la…

Numerical resonances for Schottky surfaces via Lagrange–Chebyshev approximation Open

Oscar F. Bandtlow, Anke Pohl, Torben Schick, Alexander Weiße · 2020

We present a numerical method to calculate resonances of Schottky surfaces based on Selberg theory, transfer operator techniques and Lagrange–Chebyshev approximation. This method is an alternative to the method based on periodic orbit expa…

Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy Open

Ksenia Fedosova, Anke Pohl · 2020

Eisenstein series twisted with non-expanding cusp monodromies Open

Ksenia Fedosova, Anke Pohl · 2020

Die Ansprechpartnerinnen und Ansprechpartner der DMV Open

Hinrich Lorenzen, U Oldenburg, Daniel Grieser, Anke Pohl, Michael Plum , et al. · 2019

Eigenfunctions of transfer operators and automorphic forms for Hecke triangle groups of infinite covolume Open

Roelof W. Bruggeman, Anke Pohl · 2019

We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohom…

Dynamics of geodesics, and Maass cusp forms Open

Anke Pohl, Don Zagier · 2019

The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide aud…

Fractal Weyl bounds and Hecke triangle groups Open

Frédéric Naud, Anke Pohl, Louis Soares · 2019

Let $Γ_{w}$ be a non-cofinite Hecke triangle group with cusp width $w>2$ and let $\varrho\colonΓ_w\to U(V)$ be a finite-dimensional unitary representation of $Γ_w$. In this note we announce a new fractal upper bound for the Selberg zeta fu…

Zero is a resonance of every Schottky surface Open

Alexander Adam, Anke Pohl, Alexander Weiße · 2018

For certain spectral parameters we find explicit eigenfunctions of transfer operators for Schottky surfaces. Comparing the dimension of the eigenspace for the spectral parameter zero with the multiplicity of topological zeros of the Selber…

A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions Open

Alexander Adam, Anke Pohl · 2018

Over the last few years Pohl (partly jointly with coauthors) has developed dual ‘slow/fast’ transfer operator approaches to automorphic functions, resonances, and Selberg zeta functions for a certain class of hyperbolic surfaces $\unicode[…

The category of reduced orbifolds in local charts Open

Anke Pohl · 2017

It is well-known that reduced smooth orbifolds and proper effective foliation Lie groupoids form equivalent categories. However, for certain recent lines of research, equivalence of categories is not sufficient. We propose a notion of maps…

Isomorphisms between eigenspaces of slow and fast transfer operators Open

Alexander Adam, Anke Pohl · 2016

For any Hecke triangle surface $\Gamma\backslash\mathbb{H}$ of finite or infinite area and any finite-dimensional unitary representation $\chi$ of the Hecke triangle group $\Gamma$ there had been constructed two families of Ruelle-like tra…

Symbolic dynamics, automorphic functions, and Selberg zeta functions with unitary representations Open

Anke Pohl · 2016

Using Hecke triangle surfaces of finite and infinite area as examples, we present techniques for thermodynamic formalism approaches to Selberg zeta functions with unitary finite-dimensional representations $(V,χ)$ for hyperbolic surfaces (…

The sup-norm problem on the Siegel modular space of rank two Open

Valentin Blomer, Anke Pohl · 2016

Let F be a square integrable Maass form on the Siegel upper half space of rank 2 for the Siegel modular group Sp(4, Z) with Laplace eigenvalue lambda. If, in addition, F is a joint eigenfunction of the Hecke algebra, we show a power-saving…

A geometric reduction theory for indefinite binary quadratic forms over $\mathbb{Z}[λ]$ Open

Anke Pohl, Verena Spratte · 2015

Gauss' classical reduction theory for indefinite binary quadratic forms over $\mathbb{Z}$ has originally been proven by means of purely algebraic and arithmetic considerations. It was later discovered that this reduction theory is closely …

A geometric reduction theory for indefinite binary quadratic forms over $\mathbb{Z}[\lambda]$ Open

Anke Pohl, Verena Spratte · 2015

Gauss' classical reduction theory for indefinite binary quadratic forms over $\mathbb{Z}$ has originally been proven by means of purely algebraic and arithmetic considerations. It was later discovered that this reduction theory is closely …

Amount of failure of upper-semicontinuity of entropy in non-compact rank-one situations, and Hausdorff dimension Open

Shirali Kadyrov, Anke Pohl · 2015

Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\unicode[STIX]{x1D6E4}\setminus G$ , where $G$…

Symbolic dynamics, automorphic functions, and Selberg zeta functions\n with unitary representations Open

Anke Pohl · 2015

Using Hecke triangle surfaces of finite and infinite area as examples, we\npresent techniques for thermodynamic formalism approaches to Selberg zeta\nfunctions with unitary finite-dimensional representations $(V,\\chi)$ for\nhyperbolic sur…

Escape of mass and entropy for diagonal flows in real rank one situations Open

Manfred Einsiedler, Shirali Kadyrov, Anke Pohl · 2015

Let $G$ be a connected semisimple Lie group of real rank 1 with finite center, let $Γ$ be a non-uniform lattice in $G$ and $a$ any diagonalizable element in $G$. We investigate the relation between the metric entropy of $a$ acting on the h…

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