Moments of the distribution of k$k$-free numbers in short intervals and arithmetic progressions

被引：1

作者：

Nunes, Ramon M. ^{[1
]}

机构：

[1] Univ Fed Ceara, Dept Matemat, Av Humberto Monte S-N,Campus Pici Bloco 914, BR-60440900 Fortaleza, Ceara, Brazil

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2022年 / 54卷 / 04期

关键词：

D O I：

10.1112/blms.12628

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show estimates for the distribution of k$k$-free numbers in short intervals and arithmetic progressions that, in certain ranges, agree with a conjecture by Montgomery.

引用

页码：1282 / 1298

页数：17

共 50 条

[1] Average distribution of k-free numbers in arithmetic progressions
Liu, Kui
Shparlinski, Igor E.
Zhang, Tianping
[J]. MATHEMATISCHE NACHRICHTEN, 2020, 293 (08) : 1505 - 1514
[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] AN AVERAGE THEOREM FOR TUPLES OF k-FREE NUMBERS IN ARITHMETIC PROGRESSIONS
Parry, Tomos
[J]. MATHEMATIKA, 2021, 67 (01) : 1 - 35
[7] DISTRIBUTION IN THE MEAN OF ARITHMETIC FUNCTIONS IN SHORT INTERVALS IN PROGRESSIONS
TIMOFEEV, NM
[J]. MATHEMATICS OF THE USSR-IZVESTIYA, 1987, 51 (02): : 315 - 335
[8] B-free numbers in short arithmetic progressions
Alkan, E
Zaharescu, A
[J]. JOURNAL OF NUMBER THEORY, 2005, 113 (02) : 226 - 243
[9] THE DISTRIBUTION OF r-FREE NUMBERS IN ARITHMETIC PROGRESSIONS
Gibson, Jason
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2014, 10 (03) : 559 - 563
[10] DISTRIBUTION OF MOMENTS OF HURWITZ CLASS NUMBERS IN ARITHMETIC PROGRESSIONS AND HOLOMORPHIC PROJECTION
Kane, Ben
Pujahari, Sudhir
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 376 (08) : 5503 - 5519

← 1 2 3 4 5 →