On a Generalization of Euler's Function φ(<i>n</i> )‡

H. Davenport

Type: Article

Publication Date: 1933-01-01

Citations: 15

DOI: https://doi.org/10.1112/jlms/s1-8.1.32-s

Abstract

I am indebted to Mr. A. E. Ingham for pointing out to me that the last equation in (9) is not generally true. The results are not affected, and the matter is brought into order by reading for the line following (9): “where |ε(n)| ⩽ 1 if λ ⩾ 0”, and by replacing (10) by φ a ( n ) = n a φ ( n ) a + 1 + n a a + 1 ∑ r = 1 a - 1 ( a + 1 r + 1 ) B r + 1 n - r ∏ p | n ( 1 - p r ) I am also indebted to Dr. Walfisz for pointing out to me that the expression for φα(n in (c) of Theorem 1 should have a term {nα φ(n);/(α + 1) added to it. The equation for S (d) at the top of p. 293 is in fact incorrect; a term dα+1/(α + 1) has been omitted from its right-hand side.

Locations

Journal of the London Mathematical Society - View - PDF

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