On a sum involving the Euler function

JOURNAL OF NUMBER THEORY

卷:202

Article

Bordelles, Olivier¹  Dai, Lixia²  Pan, Hao⁴  Shparlinski, Igor E.³ 

[1] 2 Allee Combe, F-43000 Aiguilhe, France

[2] Nanjing Normal Univ, Sch Math Sci, Nanjing 210046, Jiangsu, Peoples R China

[3] Univ New South Wales, Dept Pure Math, Sydney, NSW 2052, Australia

[4] Nanjing Univ Finance & Econ, Sch Appl Math, Nanjing 210046, Jiangsu, Peoples R China

关键词: Euler function;    Integer part;    Reciprocals;    Exponent pair;   

DOI  :  10.1016/j.jnt.2019.01.006

来源: Elsevier

【 摘 要 】

We obtain reasonably tight upper and lower bounds on the sum Sigma(n <= x) phi (left perpendicularx/nright perpendicular), involving the Euler functions phi and the integer parts LxInd of the reciprocals of integers. For slower growing arithmetic functions f we obtain asymptotic formulas for similar sums of f (left perpendicularx/rright perpendicular). These are analogues of a series of previous results for sequences involving the integer part functions such Beatty and Piatetski-Shapiro sequences. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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