Article
Uniform Distribution of Some Ratios Involving the Number of Prime and Integer Divisors
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Abstract
We show that the fractional parts of the ratios n/ω(n), n/aω(n), n/τ(n) and n/aτ(n), where a ≥ 2 is a fixed integer and, as usual, ω(n) and τ(n) denote the number of prime divisors and the total number of divisors of n > 1, respectively, are uniformly distributed in the unit interval [0, 1]. This complements results of several authors about the scarcity of integral values taken by the above fractions.
Keywords
sequence, fractional part, divisor, prime divisor, uniform distribution.
Citation
Luca, F. & Shparlinski, I. E. (2006). Uniform distribution of some ratios involving the number of prime and integer divisors. Uniform Distribution Theory, 1(1), 15–26.
F. Luca and I. E. Shparlinski, “Uniform distribution of some ratios involving the number of prime and integer divisors,” Uniform Distribution Theory, vol. 1, no. 1, pp. 15–26, 2006.
Luca F, Shparlinski IE. Uniform distribution of some ratios involving the number of prime and integer divisors. Uniform Distribution Theory. 2006;1(1):15–26.
Luca, F. and Shparlinski, I. E. (2006), ‘Uniform distribution of some ratios involving the number of prime and integer divisors’, Uniform Distribution Theory, 1(1), pp. 15–26.
Luca, Florian, and Igor E. Shparlinski. “Uniform Distribution of Some Ratios Involving the Number of Prime and Integer Divisors.” Uniform Distribution Theory, vol. 1, no. 1, 2006, pp. 15–26.
Luca, Florian, and Igor E. Shparlinski. “Uniform Distribution of Some Ratios Involving the Number of Prime and Integer Divisors.” Uniform Distribution Theory 1, no. 1 (2006): 15–26.
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Published by: Engineering Journals
