Continuous Distribution Arising From the Three Gaps Theorem

Geremías Polanco; Daniel Schultz; Alexandru Zaharescu

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arXiv · 1511.09399

Continuous Distribution Arising From the Three Gaps Theorem

Geremías Polanco·Daniel Schultz·Alexandru Zaharescu

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Abstract

The well known Three Gap Theorem states that there are at most three gap sizes in the sequence of fractional parts $\{αn\}_{n<N}$ . It is known that if one averages over α, the distribution becomes continuous. We present an alternative approach, which establishes this averaged result and also provides good bounds for the error terms.

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Geremías Polanco, Daniel Schultz, Alexandru Zaharescu. 2015-11-30. Continuous Distribution Arising From the Three Gaps Theorem. https://arxiv.org/abs/1511.09399

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