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Sign changes of error terms related to the Euler function

Part of: Multiplicative number theory

Published online by Cambridge University Press:  26 February 2010

Yuk-Kam Lau
Yuk-Kam Lau
Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hone Kong.
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Extract

Let φ(n) be the Euler function (i.e., φ(n) denotes the number of integers less than n which are relatively prime to n), and define

These functions were extensively studied by several mathematicians. One of the problems investigated concerns their sign changes. We say that a function fx) has a sign change at x = x0 if f(x0 −) f(x0 +) < 0, and f(x) has a sign change on the integer n if (n)f(n+1) < 0. The numbers of sign changes and sign changes on integers of f(x) in the interval [1, T] are denoted by Xf(T) and Nf(T), respectively.

MSC classification

Secondary: 11N64: Other results on the distribution of values or the characterization of arithmetic functions
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 391 - 395
Copyright
Copyright © University College London 1999

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References

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