Article
On Sequences Involving Primes
Authors
Abstract
In this paper we give the set of distribution functions of f(pn) mod1 for a special class of functions f(x). Also, we generalize a result on distri- bution functions shown by O. Strauch and O. Blaˇzekova´ to a multi-dimensional case. Applying it, we prove that every uniform distributed sequence xn mod1 and log pn mod1 is statistically independent. By combining this and a result of G. Rauzy we derive that the sequences pnθ +log pn and pnθ +pn/n are uniformly distributed mod1 with irrational θ.
Keywords
Distribution function, uniform distribution mod1, prime numbers.
Citation
Ohkubo, Y. (2011). On sequences involving primes. Uniform Distribution Theory, 6(2), 221–238.
Y. Ohkubo, “On sequences involving primes,” Uniform Distribution Theory, vol. 6, no. 2, pp. 221–238, 2011.
Ohkubo Y. On sequences involving primes. Uniform Distribution Theory. 2011;6(2):221–238.
Ohkubo, Y. (2011), ‘On sequences involving primes’, Uniform Distribution Theory, 6(2), pp. 221–238.
Ohkubo, Yukio. “On Sequences Involving Primes.” Uniform Distribution Theory, vol. 6, no. 2, 2011, pp. 221–238.
Ohkubo, Yukio. “On Sequences Involving Primes.” Uniform Distribution Theory 6, no. 2 (2011): 221–238.
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Published by: Engineering Journals
