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DISTRIBUTION OF A SPARSE SET OF FRACTIONS MODULO q

Published online by Cambridge University Press:  09 April 2001

CRISTIAN COBELI  and
ALEXANDRU ZAHARESCU
CRISTIAN COBELI
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania
ALEXANDRU ZAHARESCU
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania Institute for Advanced Study School of Mathematics, Olden Lane, Princeton, NJ 08540, USA; e-mail: [email protected]
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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.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 2 , March 2001 , pp. 138 - 148
Copyright
© The London Mathematical Society 2001

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