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DISTRIBUTION OF A SPARSE SET OF FRACTIONS MODULO q
Published online by Cambridge University Press: 09 April 2001
Abstract
The distribution on the torus ℝ/ℤ of a set of fractions of the form
(formula here)
is investigated, where q is a large integer, m is the inverse of m modulo q, R(x) is a rational function defined modulo q, and [Uscr ], [Mscr ], [Nscr ] are subsets of {1,…,q}. Under some natural assumptions, it is shown that the set [Rscr ] is uniformly distributed on ℝ/ℤ.
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- © The London Mathematical Society 2001
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