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The distribution of fractional parts of sequences αn²

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If you have a question about this talk, please contact Boris Bukh.

If α is irrational, the fractional parts of the sequence αn², for n=1,2,3,..., are uniformly distributed, as was shown by Weyl in 1916. However their distribution on a finer scale is not fully understood. This talk describes the conjecture that for most values of α the sequence has a Poisson distribution. In particular we will look at the pair correlation of nearby elements in the sequence.

This talk is part of the Discrete Analysis Seminar series.

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