Means of some arithmetical functions on shifted smooth numbers in arithmetic progression

被引：0

作者：

Khadija Mbarki

Walid Wannes

机构：

[1] Faculty of Sciences of Monastir,Department of Mathematics

[2] University of Sfax,Faculty of Sciences of Sfax

来源：

Proceedings - Mathematical Sciences | 2019年 / 129卷

关键词：

Exponential sum; smooth numbers; sum of digits function; 11A63; 11L03; 11N05;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We provide asymptotic estimates for sums of some arithmetical functions taken over shifted smooth numbers in arithmetic progression related to the sum of digits function. Our results are based on various estimates on the distribution of smooth numbers in arithmetic progressions which are due to G Tenenbaum, Stephanie S Loiperdinger and Igor E Shparlinski.

引用

共 10 条

[1] Means of some arithmetical functions on shifted smooth numbers in arithmetic progression
Mbarki, Khadija
Wannes, Walid
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2019, 129 (04):
[2] ON THE DISTRIBUTION OF THE EULER FUNCTION OF SHIFTED SMOOTH NUMBERS
Loiperdinger, Stefanie S.
Shparlinski, Igor E.
COLLOQUIUM MATHEMATICUM, 2010, 120 (01) : 139 - 148
[3] Smooth numbers and the norms of arithmetic Dirichlet convolutions
Codeca, Paolo
Nair, Mohan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 347 (02) : 400 - 406
[4] On a paper of K. Soundararajan on smooth numbers in arithmetic progressions
Harper, Adam J.
JOURNAL OF NUMBER THEORY, 2012, 132 (01) : 182 - 199
[5] Product of Some Polynomials and Arithmetic Functions
Noppakaew, Passawan
Pongsriiam, Prapanpong
JOURNAL OF INTEGER SEQUENCES, 2023, 26 (09)
[6] On Some Sums Involving Small Arithmetic Functions
Zhai, Wen Guang
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2024, 40 (10) : 2497 - 2518
[7] On the average of some arithmetical functions under a constraint on the sum of digits of squares
Aloui, Karam
HIROSHIMA MATHEMATICAL JOURNAL, 2016, 46 (01) : 37 - 54
[8] On the order of magnitude of some arithmetical functions under digital constraint I
Aloui, Karam
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2015, 125 (04): : 457 - 476
[9] ON THE ORDER OF MAGNITUDE OF SOME ARITHMETICAL FUNCTIONS UNDER DIGITAL CONSTRAINT II
Aloui, Karam
MATHEMATICAL REPORTS, 2022, 24 (03): : 403 - 423
[10] On the order of magnitude of some arithmetical functions under digital constraint I
KARAM ALOUI
Proceedings - Mathematical Sciences, 2015, 125 : 457 - 476

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