B-free numbers in short arithmetic progressions

被引:11
|
作者
Alkan, E [1 ]
Zaharescu, A [1 ]
机构
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
关键词
B-free numbers; arithmetic progressions; exponential sums;
D O I
10.1016/j.jnt.2004.10.003
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Given a sequence B of relatively prime positive integers with the sum of inverses finite, we investigate the problem of finding B-free numbers in short arithmetic progressions. (c) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码:226 / 243
页数:18
相关论文
共 50 条
  • [1] Number of B-free numbers in short intervals
    Zhai, WG
    [J]. CHINESE SCIENCE BULLETIN, 2000, 45 (03): : 208 - 212
  • [2] DISTRIBUTION OF B-FREE NUMBERS
    PLAKSIN, VA
    [J]. MATHEMATICAL NOTES, 1990, 47 (1-2) : 162 - 169
  • [3] SQUARE-FREE NUMBERS IN ARITHMETIC PROGRESSIONS
    CROFT, MJ
    [J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1975, 30 (FEB) : 143 - 159
  • [4] Sparse variance for -free numbers in arithmetic progressions
    Dehnert, Fabian
    [J]. MONATSHEFTE FUR MATHEMATIK, 2015, 177 (03): : 373 - 396
  • [5] SQUARE-FREE NUMBERS IN ARITHMETIC PROGRESSIONS
    FLUCH, W
    [J]. MONATSHEFTE FUR MATHEMATIK, 1968, 72 (05): : 427 - &
  • [6] 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
  • [7] ARITHMETIC PROGRESSIONS OF b-NIVEN NUMBERS
    Grundman, Helen G.
    Harrington, Joshua
    Wong, Tony W. H.
    [J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2024, 54 (03) : 723 - 733
  • [8] Arithmetic Progressions of b-Prodigious Numbers
    Gohn, Michael
    Lebiere, Sophia
    Shappell, Kyla
    Harrington, Joshua
    Samamah, Hani
    Wong, Tony W. H.
    [J]. JOURNAL OF INTEGER SEQUENCES, 2022, 25 (08)
  • [9] Twins of k-free numbers in arithmetic progressions
    Zaizhao Meng
    [J]. Acta Mathematica Hungarica, 2011, 130 : 223 - 253
  • [10] A variance for k-free numbers in arithmetic progressions
    Vaughan, R. C.
    [J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2005, 91 : 573 - 597