TY - JOUR
T1 - Continuous distributions arising from the Three Gap Theorem
AU - Polanco, Geremías
AU - Schultz, Daniel
AU - Zaharescu, Alexandru
N1 - Publisher Copyright:
© 2016 World Scientific Publishing Company.
PY - 2016/11/1
Y1 - 2016/11/1
N2 - 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.
AB - 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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U2 - 10.1142/S1793042116501074
DO - 10.1142/S1793042116501074
M3 - Article
AN - SCOPUS:84951986407
SN - 1793-0421
VL - 12
SP - 1743
EP - 1764
JO - International Journal of Number Theory
JF - International Journal of Number Theory
IS - 7
ER -