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Cristian Cobeli, Alexandru Zaharescu, Distribution of a Sparse Set of Fractions Modulo q, Bulletin of the London Mathematical Society, Volume 33, Issue 2, March 2001, Pages 138–148, https://doi.org/10.1112/blms/33.2.138
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Abstract
The distribution on the torus R/Z of a set of fractions of the form
is investigated, where q is a large integer, is the inverse of m modulo q, R(x) is a rational function defined modulo q, and U, M, N are subsets of {1,…,q}. Under some natural assumptions, it is shown that the set R is uniformly distributed on R/Z.
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