Lorenz Frühwirth

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math.NT2023

Limit laws for cotangent and Diophantine sums

Bence Borda, Lorenz Frühwirth, Manuel Hauke

Limit laws for ergodic averages with a power singularity over circle rotations were first proved by Sinai and Ulcigrai, as well as Dolgopyat and Fayad. In this paper, we prove limi…

math.NT2023

On the metric upper density of Birkhoff sums for irrational rotations

Lorenz Frühwirth, Manuel Hauke

This article examines the value distribution of $S_{N} (f, α) := \sum_{n = 1}^{N} f (n α)$ for almost every $α$ where $N \in N$ is ranging over a long interval and $f$ is a $1$ -p…