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The Existence of a Distribution Function for an Error Term Related to the Euler Function

Published online by Cambridge University Press:  20 November 2018

Paul Erdös  and
H. N. Shapiro
Paul Erdös
Affiliation:
Notre Dame University
H. N. Shapiro
Affiliation:
New York University
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The average order of the Euler function ϕ(n), the number of integers less than n which are relatively prime to n, raises many difficult and still unanswered questions. Thus, for

1.1,

and

1.2,

it is known that R(x) = O(x log x) and H(x) = O(log x). However, though these results are quite old, they were not improved until recently.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 63 - 75
Copyright
Copyright © Canadian Mathematical Society 1955

References

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