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.
Original language | English (US) |
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Pages (from-to) | 1743-1764 |
Number of pages | 22 |
Journal | International Journal of Number Theory |
Volume | 12 |
Issue number | 7 |
DOIs | |
State | Published - Nov 1 2016 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory