On an error term of Landau. II. (English) Zbl 0584.10027

[Part I, cf. Indian J. Pure Appl. Math. 13, 882-885 (1982; Zbl 0494.10033).]
The author studies averages of the error terms \(E_ 0(x)\) and \(E_ 1(x)\) in the asymptotic formulas \[ \sum_{n\leq x}1/\phi (n)=A(\log x+B)+E_ 0(x)\quad and\quad \sum_{n\leq x}n/\phi (n)=Ax- \log x+E_ 1(x) \] where A and B are specified constants. Typical results are \[ \int^{x}_{1}E_ 0(t) dt=-\log x+O(1)\quad and\quad \int^{x}_{1}E_ 1(t) dt=\alpha x+O(x^{4/5}), \] where \(\alpha\) is a specified negative constant. For \(E_ 0(x)\), \(\Omega\) results are also given.
Reviewer: T.M.Apostol


11N37 Asymptotic results on arithmetic functions


Zbl 0494.10033
Full Text: DOI