On the distribution of Sudler products and Birkhoff sums for the irrational rotation

Bence Borda

We study the value distribution of the Sudler product ${\prod }_{n=1}^N|2\sin (\pi n\alpha )|$ and the Diophantine product ${\prod }_{n=1}^N(2e\Vert n\alpha \Vert )$ for various irrational $\alpha$, as $N$ ra…