Average distribution of k-free numbers in arithmetic progressions

被引：2

作者：

Liu, Kui ^{[1
]}

Shparlinski, Igor E. ^{[2
]}

Zhang, Tianping ^{[3
]}

机构：

[1] Qingdao Univ, Sch Math & Stat, 308 Ningxia Rd, Qingdao 266071, Shandong, Peoples R China

[2] Univ New South Wales, Dept Pure Math, Sydney, NSW 2052, Australia

[3] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710119, Shaanxi, Peoples R China

来源：

MATHEMATISCHE NACHRICHTEN | 2020年 / 293卷 / 08期

基金：

澳大利亚研究理事会; 中国国家自然科学基金;

关键词：

arithmetic progressions; average value; k-free numbers;

D O I：

10.1002/mana.201900006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain a new bound on the average value of the error term in the asymptotic formula for the number of k-free numbers in arithmetic progressions. In particular, we improve the results of J. Gibson (2014) and C. Hooley (1975).

引用

页码：1505 / 1514

页数：10

共 50 条

[1] AN AVERAGE THEOREM FOR TUPLES OF k-FREE NUMBERS IN ARITHMETIC PROGRESSIONS
Parry, Tomos
[J]. MATHEMATIKA, 2021, 67 (01) : 1 - 35
[2] Twins of k-free numbers in arithmetic progressions
Zaizhao Meng
[J]. Acta Mathematica Hungarica, 2011, 130 : 223 - 253
[3] A variance for k-free numbers in arithmetic progressions
Vaughan, R. C.
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2005, 91 : 573 - 597
[4] TWINS OF k-FREE NUMBERS IN ARITHMETIC PROGRESSIONS
Meng, Z.
[J]. ACTA MATHEMATICA HUNGARICA, 2011, 130 (03) : 223 - 253
[5] A variance for k-free numbers in arithmetic progressions of given modulus
Parry, Tomos
[J]. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2021, 33 (02): : 317 - 360
[6] THE DISTRIBUTION OF k-FREE NUMBERS
Mossinghoff, Michael J.
E Silva, Tomas Oliveira
Trudgian, Timothy S.
[J]. MATHEMATICS OF COMPUTATION, 2021, 90 (328) : 907 - 929
[7] THE DISTRIBUTION OF k-FREE NUMBERS
Baker, R. C.
Powell, K.
[J]. ACTA MATHEMATICA HUNGARICA, 2010, 126 (1-2) : 181 - 197
[8] The distribution of k-free numbers
R. C. Baker
K. Powell
[J]. Acta Mathematica Hungarica, 2010, 126 : 181 - 197
[9] About k-free Numbers in arithmetic Sequences
Bundschuh, Peter
[J]. ELEMENTE DER MATHEMATIK, 2019, 74 (01) : 31 - 35
[10] Moments of the distribution of k$k$-free numbers in short intervals and arithmetic progressions
Nunes, Ramon M.
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2022, 54 (04) : 1282 - 1298

← 1 2 3 4 5 →