Uniform distribution of the fractional part of the average prime divisor

WD Banks*, Moubariz Z. Garaev, F Luca, Igor Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We estimate exponential sums with the function p(n) defined as the average of the prime divisors of an integer n >= 2 (we also put p(1) = 0). Our bound implies that the fractional parts of the numbers {p(n) : n >= 1} are uniformly distributed over the unit interval. We also estimate the discrepancy of the distribution, and we determine the precise order of the counting function of the set of those positive integers n such that p(n) is an integer.

Original languageEnglish
Pages (from-to)885-901
Number of pages17
JournalForum Mathematicum
Issue number6
Publication statusPublished - 2005



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