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Poisson statistics via the Chinese remainder theorem
[article]

2005
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arXiv
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pre-print

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 have Poisson spacings. We also study the spacings of subsets of Z/q_1q_2Z that are created via the

arXiv:math/0412135v2
fatcat:yxwixjmksvb4neou55k2lec5ni