The distribution of spacings between the fractional parts of n2α
By Z. Rudnick, Peter Sarnak, A. Zaharescu. International mathematics research notices, 2000
136 citations recorded by the source corpus.
We study the distribution of spacings between the fractional parts of $n^d\alpha $. For $\alpha $ of high enough Diophantine type we prove a necessary and sufficient condition for $n^d\alpha \mod 1, 1\leq n\leq N,$ to be Poissonian as $N\to \infty $ along a suitable subsequence.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/6ff496b90bfbec870af0555473979cdfa94490ce
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Modular hyperbolas (2011, background): “7 Pair Correlation of Fractional Parts of αn(2) It is known, see [146, 160], that the spacings between the fractional parts of the sequence αn(2), n = 1, 2, .”
- On pair correlation and discrepancy (2016, background): “Introduction The concept of Poissonian pair correlations for a sequence (xn)n≥1 in [0, 1) was introduced by Rudnick and Sarnak in [5], and has been intensively studied by several authors over the last years (see for instance [2, 3, 6, 7, 8]).”