Oscillations of the remainder term related to the Euler totient function

[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.

[发布日期] 2010-12-01

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