Publications by Florian Karl Richter

ON THE MAXIMAL SPECTRAL TYPE OF NILSYSTEMS

Let (G/Γ, Ra) be an ergodic k-step nilsystem for k ≥ 2. We adapt an argument of Parry [Topology 9 (1970), pp. 217–224] to show that L2 (G/Γ) decomposes as a sum of a subspace with discrete spectrum and a subspace of Lebesgue spectrum with infinite multipli ...

2024

INTERPOLATION SETS FOR DYNAMICAL SYSTEMS

Florian Karl Richter

. Originating in harmonic analysis, interpolation sets were first studied in dynamics by Glasner and Weiss in the 1980s [Israel J. Math. 44 (1983), pp. 345-360]. A set S subset of N is an interpolation set for a class of topological dynamical systems C if ...

AMER MATHEMATICAL SOC2024

On the Local Fourier Uniformity Problem for Small Sets

Florian Karl Richter

We consider vanishing properties of exponential sums of the Liouville function λ of the form lim lim sup log1X mΣ≤X m1 sup α∈C|||| H1 Σ λ(m + h)e2πihα |||| = 0, H→∞ X→∞ h≤H where C ⊂ T. The case C = T corresponds to the local 1-Fourier uniformity conjectur ...

2024

A Proof of Erdős’s B + B + T Conjecture

Florian Karl Richter

We show that every set A of natural numbers with positive upper Banach density can be shifted to contain the restricted sumset (formula presented) for some infinite set B ⊂ A. ...

2024

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

Multiple ergodic averages along functions from a Hardy field: Convergence, recurrence and combinatorial applications

Florian Karl Richter

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [19,21] and obtain combinatorial applications ...

San Diego2024

Zero-one laws for eventually always hitting points in rapidly mixing systems

Florian Karl Richter

In this work we study the set of eventually always hitting points in shrinking target systems. These are points whose long orbit segments eventually hit the corresponding shrinking targets for all future times. We focus our attention on systems where trans ...

Int Press Boston, Inc2023

Infinite Sumsets In Sets With Positive Density

Florian Karl Richter

2023