On the distribution of k-th power free integers

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Abstract

Let X (k)(n) be the indicator function of the set of k-th power free integers. In this paper, we study refinements of the density theorem, ζ being the Riemann zeta function. The method we take here is a compactification of ℤ; we extend S (k) N to a random variable on a probability space (ℤ̂, λ) in a natural way, where Ẑ is the ring of finite integral adeles and λ is the shift invariant normalized Haar measure. Then we investigate the rate of L 2-convergence of S (k) N, from which the above asymptotic result is derived.

Original languageEnglish
Pages (from-to)1027-1045
Number of pages19
JournalOsaka Journal of Mathematics
Volume48
Issue number4
Publication statusPublished - 2011 Dec

ASJC Scopus subject areas

  • Mathematics(all)

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