On the distribution of squarefree integers in arithmetic progressions

被引：6
|
作者：
Le Boudec, Pierre [1 ]
机构：
[1] EPFL SB MATHGEOM TAN MA C3 604, Batiment MA,Stn 8, CH-1015 Lausanne, Switzerland
来源：
MATHEMATISCHE ZEITSCHRIFT | 2018年 / 290卷 / 1-2期
关键词：
Squarefree integers; Arithmetic progressions; Variance; FREE NUMBERS;
D O I：
10.1007/s00209-017-2023-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
investigate the error term of the asymptotic formula for the number of squarefree integers up to some bound, and lying in some arithmetic progression a (mod q). In particular, we prove an upper bound for its variance as a varies over (Z/qZ)(x) which considerably improves upon earlier work of Blomer.
引用
收藏
页码：421 / 429
页数：9
相关论文
共 50 条
  • [1] On the distribution of squarefree integers in arithmetic progressions
    Pierre Le Boudec
    [J]. Mathematische Zeitschrift, 2018, 290 : 421 - 429
  • [2] SMOOTH SQUAREFREE AND SQUAREFULL INTEGERS IN ARITHMETIC PROGRESSIONS
    Munsch, Marc
    Shparlinski, Igor E.
    Yau, Kam Hung
    [J]. MATHEMATIKA, 2020, 66 (01) : 56 - 70
  • [3] REMAINDER ESTIMATES FOR SQUAREFREE INTEGERS IN ARITHMETIC PROGRESSIONS
    ORR, RC
    [J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (01): : 252 - &
  • [4] Arithmetic Progressions, Prime Numbers, and Squarefree Integers
    Stuart Clary
    Jacek Fabrykowski
    [J]. Czechoslovak Mathematical Journal, 2004, 54 : 915 - 927
  • [5] Squarefree Integers in Arithmetic Progressions to Smooth Moduli
    Mangerel, Alexander P.
    [J]. FORUM OF MATHEMATICS SIGMA, 2021, 9
  • [6] Arithmetic progressions, prime numbers, and squarefree integers
    Clary, S
    Fabrykowski, J
    [J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2004, 54 (04) : 915 - 927
  • [7] On the variance of squarefree integers in short intervals and arithmetic progressions
    Ofir Gorodetsky
    Kaisa Matomäki
    Maksym Radziwiłł
    Brad Rodgers
    [J]. Geometric and Functional Analysis, 2021, 31 : 111 - 149
  • [8] ON THE VARIANCE OF SQUAREFREE INTEGERS IN SHORT INTERVALS AND ARITHMETIC PROGRESSIONS
    Gorodetsky, Ofir
    Matomaki, Kaisa
    Radziwill, Maksym
    Rodgers, Brad
    [J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2021, 31 (01) : 111 - 149
  • [9] SQUAREFREE NUMBERS IN ARITHMETIC PROGRESSIONS
    WARLIMONT, R
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1980, 22 (AUG): : 21 - 24
  • [10] SQUAREFREE NUMBERS IN ARITHMETIC PROGRESSIONS
    WARLIMONT, R
    [J]. MONATSHEFTE FUR MATHEMATIK, 1972, 76 (03): : 272 - +
12345