# Fast and slow points of Birkhoff sums

Abstract : We investigate the growth rate of the Birkhoff sums $S_{n,\alpha}f(x)=\sum_{k=0}^{n-1}f(x+k\alpha)$, where $f$ is a continuous function with zero mean defined on the unit circle $\mathbb T$ and $(\alpha,x)$ is a typical'' element of $\mathbb T^2$. The answer depends on the meaning given to the word typical''. Part of the work will be done in a more general context.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-01975709
Contributor : Frédéric Bayart <>
Submitted on : Wednesday, January 9, 2019 - 3:01:34 PM
Last modification on : Saturday, January 12, 2019 - 1:19:52 AM

### Files

bby18.pdf
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### Identifiers

• HAL Id : hal-01975709, version 1
• ARXIV : 1901.03504

### Citation

Frédéric Bayart, Zoltan Buczolich, Yanick Heurteaux. Fast and slow points of Birkhoff sums. 2019. ⟨hal-01975709⟩

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