Distribution of a sparse set of fractions modulo q

Cristian Cobeli, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


The distribution on the torus ℝ/ℤ of a set of fractions of the form script R = {um̄R(n) (mod q)/q : u ∈ script U, m ∈ script M, n ∈ script N} is investigated, where q is a large integer, m̄ is the inverse of m modulo q, R(x) is a rational function defined modulo q, and script U, script M, script N are subsets of {1, ..., q}. Under some natural assumptions, it is shown that the set script R is uniformly distributed on ℝ/ℤ.

Original languageEnglish (US)
Pages (from-to)138-148
Number of pages11
JournalBulletin of the London Mathematical Society
Issue number2
StatePublished - Mar 2001
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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