On general sums involving the floor function with applications to k-free numbers

被引：1
|
作者：
Zhang, Wei [1 ]
机构：
[1] Henan Univ, Sch Math & Stat, Kaifeng 475004, Henan, Peoples R China
来源：
LITHUANIAN MATHEMATICAL JOURNAL | 2023年 / 63卷 / 04期
关键词：
asymptotic formulas; exponential sums; sequences and sets;
D O I：
10.1007/s10986-023-09611-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider sums related to the floor function. We improve previous results for some special arithmetic functions considered by O. Bordelles [On certain sums of number theory, Int. J. Number Theory, 18(9):2053- 2074, 2022], J. Stucky [The fractional sum of small arithmetic functions, J. Number Theory, 238:731-739, 2022], and J. Wu [Note on a paper by Bordelles, Dai, Heyman, Pan and Shparlinski, Period. Math. Hung., 80(1):95-102, 2020]. It is worth emphasizing that we use much simpler methods to give much better results than previous.
引用
收藏
页码：547 / 556
页数：10
相关论文
共 46 条
  • [1] On general sums involving the floor function with applications to k-free numbers
    Wei Zhang
    Lithuanian Mathematical Journal, 2023, 63 : 547 - 556
  • [2] MOMENT ESTIMATES FOR EXPONENTIAL SUMS OVER k-FREE NUMBERS
    Keil, Eugen
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2013, 9 (03) : 607 - 619
  • [3] THE DISTRIBUTION OF k-FREE NUMBERS
    Mossinghoff, Michael J.
    E Silva, Tomas Oliveira
    Trudgian, Timothy S.
    MATHEMATICS OF COMPUTATION, 2021, 90 (328) : 907 - 929
  • [4] THE DISTRIBUTION OF k-FREE NUMBERS
    Baker, R. C.
    Powell, K.
    ACTA MATHEMATICA HUNGARICA, 2010, 126 (1-2) : 181 - 197
  • [5] The distribution of k-free numbers
    R. C. Baker
    K. Powell
    Acta Mathematica Hungarica, 2010, 126 : 181 - 197
  • [6] On the distribution of k-free numbers and r-tuples of k-free numbers. A survey
    Tsvetkov, Radoslav
    NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2019, 25 (03) : 207 - 222
  • [7] The density of twins of k-free numbers
    Dietmann, Rainer
    Marmon, Oscar
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2014, 46 : 818 - 826
  • [8] ON GAPS BETWEEN K-FREE NUMBERS
    TRIFONOV, O
    JOURNAL OF NUMBER THEORY, 1995, 55 (01) : 46 - 59
  • [9] On the exponential sum over k-free numbers
    Brudern, J
    Granville, A
    Perelli, A
    Vaughan, RC
    Wooley, TD
    PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1998, 356 (1738): : 739 - 761
  • [10] Some new results on k-free numbers
    Meng, Zaizhao
    JOURNAL OF NUMBER THEORY, 2006, 121 (01) : 45 - 66
12345