THE DISTRIBUTION OF k-FREE NUMBERS

被引：8

作者：

Baker, R. C. ^{[1
]}

Powell, K. ^{[1
]}

机构：

[1] Brigham Young Univ, Provo, UT 84602 USA

来源：

ACTA MATHEMATICA HUNGARICA | 2010年 / 126卷 / 1-2期

关键词：

k-free number; Riemann hypothesis; exponential sum; double large sieve; SQUARE-FREE NUMBERS; EXPONENTIAL-SUMS; MONOMIALS;

D O I：

10.1007/s10474-009-9042-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let k is an element of {3, 4, 5}. Let R(k)(x) = Sigma(n <= x n is k-free) 1 - x/zeta(k). We give new upper bounds for R(k)(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.

引用

页码：181 / 197

页数：17

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