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Erdős problem 1002

For any 0<α<10<\alpha<1, let f(α,n)=1log⁡n∑1≤k≤n(12−{αk})f(\alpha,n)=\frac{1}{\log n}\sum_{1\leq k\leq n}(\tfrac{1}{2}- \{ \alpha k\}). Does f(α,n)f(\alpha,n) have an asymptotic distribution function?

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sha256:c1198521061b856d3cf238cb5250f6aa57101ccf64e4eb746e8784f2ce0b55ba
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sha256:0f14d73b2162e3670783c31cb0df8cf7ea1fe260c8d371922578375b637a7b09
Observation
sha256:8c823d621b7e1256c8e47c60a5f1c54c016a5507e6f27b2bab537f6f5f232067
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sha256:5c5d84b5e39d4b6052192d97df1b7eb7a6b7b2951ca89c2669e1dacf29d31722
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sha256:c9d14c459c518937e758918b5897dc3b22f1a55f07739afe99502f5b046c907a
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2415f78e850aeee50afdca525c6f2e0ea606f207
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