Notes on Uniform Distribution Modulo One

G. Myerson*, A. D. Pollington

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    We exhibit a sequence (un) which is not uniformly distributed modulo one even though for each fixed integer k > 2 the sequence (kun) is u.d. (mod 1). Within the set of all such sequences, we characterize those with a well-behaved asymptotic distribution function. We exhibit a sequence (un) which is u.d. (mod 1) even though no subsequence of the form {ukn+j) is u.d. (mod 1) for any k > 2. We prove that, if the subsequences (ukn) are u.d. (mod 1) for all squarefree k which are products of primes in a fixed set p, then (un) is u.d. (mod 1) if the sum of the reciprocals of the primes in p diverges. We show that this result is the best possible of its type.

    Original languageEnglish
    Pages (from-to)264-272
    Number of pages9
    JournalJournal of the Australian Mathematical Society
    Issue number2
    Publication statusPublished - 1990


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