Oscillations of the remainder term related to the Euler totient function

JOURNAL OF NUMBER THEORY

卷:130

Article

Kaczorowski, Jerzy¹  Wiertelak, Kazimierz¹ 

[1] Adam Mickiewicz Univ Poznan, Fac Math & Comp Sci, PL-61614 Poznan, Poland

关键词: Euler totient function;    Omega theorems;    Riemann Hypothesis;    Oscillations of the remainder term;   

DOI  :  10.1016/j.jnt.2010.06.010

来源: Elsevier

【 摘 要 】

We split the remainder term in the asymptotic formula for the mean of the Euler phi function into two summands called the arithmetic and the analytic part respectively. We show that the arithmetic part can be studied with a mild use of the complex analytic tools, whereas the study of the analytic part heavily depends on the properties of the Riemann zeta function and on the distribution of its non-trivial zeros in particular. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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