关于{x/p}的分布

董玲玲;翟文广;

数学学报 ›› 2009 ›› Issue (03) : 155-164.

数学学报 ›› 2009 ›› Issue (03) : 155-164. DOI: 10.12386/A2009sxxb0068
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关于{x/p}的分布

    董玲玲;翟文广;
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On the Distribution of {x/p}~

    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
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摘要

研究不等式α≤{x/p}<α+R/p(p≤x)和0≤{x/p}<α(p≤y)的解的个数问题.对前一不等式,当x~(32/47+∈)

Abstract

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.

关键词

素数定理 / 零点密度估计 / 指数和方法

Key words

prime number theorem / density of the distribution of the Riemann zeta function / method of exponential sums

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董玲玲;翟文广;. 关于{x/p}的分布. 数学学报, 2009(03): 155-164 https://doi.org/10.12386/A2009sxxb0068
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

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