Distribution of gaps between the inverses mod q

C. Cobeli, M. Vâjâitu, A. Zaharescu

Research output: Contribution to journalArticlepeer-review


Let q be a positive integer, let I = I(q) and J = J(q) be subintervals of integers in [1, q] and let M be the set of elements of I that are invertible modulo q and whose inverses lie in J. We show that when q approaches infinity through a sequence of values such that φ(q)/q → 0, the r-spacing distribution between consecutive elements of M becomes exponential.

Original languageEnglish (US)
Pages (from-to)185-203
Number of pages19
JournalProceedings of the Edinburgh Mathematical Society
Issue number1
StatePublished - Feb 2003


  • Exponential sums
  • Inverses
  • Poissonian distribution

ASJC Scopus subject areas

  • Mathematics(all)


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