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3 questions
12
votes
1
answer
617
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Convergence of the series involving Mobius functions $\sum_{k,d} \mu(d) x_{kd}$
(I originally asked this question here, but the problem appears much more difficult than I think after a moment of thought, so I think it might be more suitable to post it here. Please tell me if this ...
- 1,755
3
votes
1
answer
332
views
Rate of convergence of ergodic averages related to irrational rotation
Let $\alpha$ be an irrational number, consider the basic dynamical system $T^{n}(0) = \{n \alpha\}$ where $\{.\}$ denotes the fractional part.
Let $a < b$ be two numbers in $[0, 1]$. Then by ...
13
votes
1
answer
1k
views
Is $\varliminf_{n \rightarrow +\infty} |n \sin n| = 0$ correct, where $n$ is an integer?
Is it true that $\varliminf_{n \rightarrow +\infty} |n \sin n| = 0$, where $n$
runs over the integers?
The existence of the limes inferior follows from Dirichlet's approximation theorem,
but the ...
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