# Distribution modulo 1 of some oscillating sequences, II Academic Article

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### abstract

• For some oscillating functions, such as $$h\left( x \right) = x^\pi \log ^3 \times \cos \times$$, we consider the distribution properties modulo 1 (density, uniform distribution) of the sequence $$h\left( n \right)$$, $${n \geqq 1}$$. We obtain positive and negative results covering the case when the factor $$x^{\pi } {log}^3 x$$ is replaced by an arbitrary function $$f$$ of at most polynomial growth belonging to any Hardy field. (The latter condition may be viewed as a regularity growth condition on $$f$$.) Similar results are obtained for the subsequence $$h\left( p \right)$$, taken over the primes $$p = 2,3,5,...\;.$$

### publication date

• January 1, 1995