The distribution of k-free numbers

被引：0
|
作者：
R. C. Baker
K. Powell
机构：
[1] Brigham Young University,
来源：
Acta Mathematica Hungarica | 2010年 / 126卷
关键词：
-free number; Riemann hypothesis; exponential sum; double large sieve; 11N25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let k ∈ {3; 4; 5}. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ R_k (x) = \sum\limits_{n \leqq xnisk - free} {1 - \frac{x} {{\zeta (k)}}} . $$\end{document} We give new upper bounds for Rk(x) conditional on the Riemann hypothesis, improving work of S. W. Graham and J. Pintz. The method stays close to that devised by H. L. Montgomery and R. C. Vaughan, with the improvement depending on exponential sum results.
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页码：181 / 197
页数：16
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