arXiv subjects

Anke Pohl

Publications and source records attributed to Anke Pohl.

21 records · Page 2Linked to original sources

arXiv2016

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

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 sup-norm bound in terms of lambda (relative to the generic bound) for F restricted to a compact set. As an auxiliary result of independent interest we prove new uniform bounds for spherical functions on semisimple Lie groups.

math.NT↗

arXiv2015

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

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 related to a certain symbolic dynamics for the geodesic flow on the modular surface, and hence can also be deduced geometrically. In this article, we use certain symbolic dynamics for the geodesic flow on Hecke triangle surfaces (also the non-arithmetic ones) to develop reduction theories for the indefinite binary quadratic forms associated to Hecke triangle groups. Moreover, we propose an algorithm to decide for any $g\in {\rm PSL}_2(\mathbb{R})$ whether or not $g$ is contained in the Hecke triangle group under consideration, and provide an upper estimate for its run time.

math.NT↗

arXiv2014

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

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 homogeneous space $Γ\backslash G$ and escape of mass. Moreover, we provide bounds on the escaping mass and, as an application, we show that the Hausdorff dimension of the set of orbits (under iteration of $a$) which miss a fixed open set is not full.

math.DS↗