Poisson statistics via the Chinese Remainder Theorem

@inproceedings{Granville2006PoissonSV,
  title={Poisson statistics via the Chinese Remainder Theorem},
  author={Andrew Granville and P{\"a}r Kurlberg},
  year={2006}
}
We consider the distribution of spacings between consecutive elements in subsets of Z/qZ, where q is highly composite and the subsets are defined via the Chinese Remainder Theorem. We give a sufficient criterion for the spacing distribution to be Poissonian as the number of prime factors of q tends to infinity, and as an application we show that the value set of a generic polynomial modulo q has Poisson spacings. We also study the spacings of subsets of Z/q1q2Z that are created via the Chinese… CONTINUE READING

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