A variance for k-free numbers in arithmetic progressions of given modulus

被引：0

作者：

Parry, Tomos

机构：

来源：

JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX | 2021年 / 33卷 / 02期

关键词：

k-free number; variance; arithmetic progression;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An asymptotic formula for the variance of squarefree numbers in arithmetic progressions of given modulus was obtained by Nunes, see [9]. We improve one of the error terms as far as one would expect to be able to go.

引用

页码：317 / 360

页数：45

共 50 条

[1] A variance for k-free numbers in arithmetic progressions
Vaughan, R. C.
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2005, 91 : 573 - 597
[2] Twins of k-free numbers in arithmetic progressions
Zaizhao Meng
Acta Mathematica Hungarica, 2011, 130 : 223 - 253
[3] TWINS OF k-FREE NUMBERS IN ARITHMETIC PROGRESSIONS
Meng, Z.
ACTA MATHEMATICA HUNGARICA, 2011, 130 (03) : 223 - 253
[4] Average distribution of k-free numbers in arithmetic progressions
Liu, Kui
Shparlinski, Igor E.
Zhang, Tianping
MATHEMATISCHE NACHRICHTEN, 2020, 293 (08) : 1505 - 1514
[5] AN AVERAGE THEOREM FOR TUPLES OF k-FREE NUMBERS IN ARITHMETIC PROGRESSIONS
Parry, Tomos
MATHEMATIKA, 2021, 67 (01) : 1 - 35
[6] Sparse variance for -free numbers in arithmetic progressions
Dehnert, Fabian
MONATSHEFTE FUR MATHEMATIK, 2015, 177 (03): : 373 - 396
[7] About k-free Numbers in arithmetic Sequences
Bundschuh, Peter
ELEMENTE DER MATHEMATIK, 2019, 74 (01) : 31 - 35
[8] Variance of the k-fold divisor function in arithmetic progressions for individual modulus
Nguyen, David T.
ACTA ARITHMETICA, 2024, 212 (03) : 195 - 223
[9] VARIANCE OF THE k-FOLD DIVISOR FUNCTION IN ARITHMETIC PROGRESSIONS FOR INDIVIDUAL MODULUS
Nguyen, David T.
arXiv, 2022,
[10] THE DISTRIBUTION OF k-FREE NUMBERS
Mossinghoff, Michael J.
E Silva, Tomas Oliveira
Trudgian, Timothy S.
MATHEMATICS OF COMPUTATION, 2021, 90 (328) : 907 - 929

← 1 2 3 4 5 →