Ling Ling DONG Finance Professional College,Shandong Institute of Light Industry,Jinan 250100,P.R.China Wen Guang ZHAI School of Mathematical Sciences,Shandong Normal University,Jinan 250014,P.R.China
The aim of this paper is to study the numbers of solutions of the inequalitiesα≤{x/p} <α+R/p(p≤x) and 0≤{x/p} <α(p≤y).For the former inequality,we obtain an asymptotic formula for x~(32/47+∈) < R < x~(1-∈).For the latter inequality,we obtain an asymptotic formula for x~∈■y < x,which improves an classical result of Saffari and Vaughan.
Ling Ling DONG Finance Professional College,Shandong Institute of Light Industry,Jinan 250100,P.R.China Wen Guang ZHAI School of Mathematical Sciences,Shandong Normal University,Jinan 250014,P.R.China.
On the Distribution of {x/p}~. Acta Mathematica Sinica, Chinese Series, 2009(03): 155-164 https://doi.org/10.12386/A2009sxxb0068