Let $\alpha$ be an algebraic integer of modulus 1, and $ R_\alpha z=\alpha z$. Is $$\lim_{n\to\infty}\frac{\log\sum_{k=1}^n \Re R_\alpha^k z}{\log n}=\frac12$$ for all $z\in S^1$?
Central limit theorem for irrational rotations
Nikita Sidorov
- 2.1k
- 1
- 18
- 25