Stefan Steinerberger

activity

20232026

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Showing 2024Show all

6 papers · 1 filter

math.CA2024

Failure of Orthogonality of Rounded Fourier Bases

François Clément, Stefan Steinerberger

The purpose of this note is to prove estimates for $$ \left| \sum_{k=1}^{n} \mbox{sign} \left( \cos \left( \frac{2πa}{n} k \right) \right) \mbox{sign} \left( \cos \left( \frac{2πb}…

math.DS2024

A curious dynamical system in the plane

Stefan Steinerberger, Tony Zeng

For any irrational $α > 0$ and any initial value $z_{- 1} \in C$ , we define a sequence of complex numbers $(z_{n})_{n = 0}^{\infty}$ as follows: $z_{n}$ is $z_{n - 1} + e^{2 π i α n}$ …

math.CO2024

On differences of two harmonic numbers

Jeck Lim, Stefan Steinerberger

We prove that the existence of infinitely many $(m_{k}, n_{k}) \in N^{2}$ such that the difference of harmonic numbers $H_{m_{k}} - H_{n_{k}}$ approximates 1 well $$ \lim_{k \righta…

math.FA2024

A lower bound for the Balan--Jiang matrix problem

Afonso S. Bandeira, Dustin G. Mixon, Stefan Steinerberger

We prove the existence of a positive semidefinite matrix $A \in R^{n \times n}$ such that any decomposition into rank-1 matrices has to have factors with a large $ℓ^{1} -$ …

math.SP2024

Universal lower bounds for Dirichlet eigenvalues

Stefan Steinerberger

Let $Ω \subset R^{d}$ be a bounded domain and let $λ_{1}, λ_{2}, \dots$ denote the sequence of eigenvalues of the Laplacian subject to Dirichlet boundary conditions. We consider…

math.CO2024

On a problem involving unit fractions

Stefan Steinerberger

Erdős and Graham proposed to determine the number of subsets $S \subseteq {1, 2, \dots, n}$ with $\sum_{s \in S} 1/ s = 1$ and asked, among other things, whether that numb…