Let $f:\mathbb{R} \to \mathbb{R}$ be a continuous function with period $T$,where $T$ is an irrational number,and the integral of $f$ over one period is $0$.
Can we conclude that $\sum_{k=0}^N f(k)$ is bounded?
Let $f:\mathbb{R} \to \mathbb{R}$ be a continuous function with period $T$,where $T$ is an irrational number,and the integral of $f$ over one period is $0$.
Can we conclude that $\sum_{k=0}^N f(k)$ is bounded?
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