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Frequency of oscillations of an error term related to the Euler function

Part of: Multiplicative number theory

Published online by Cambridge University Press:  26 February 2010

Yuk-Kam Lau  and
Y. -F. S. Pétermann
Yuk-Kam Lau
Affiliation:
Institut Élie Cartan, Université Henri Poincaré (Nancy 1), 54506 Vandœuvre-lès-Nancy Cedex, France. E-mail: [email protected]
Y. -F. S. Pétermann
Affiliation:
Université de Genève, Section de Mathématiques, 2–4, rue de Lièvre, C.P. 240, 1211 Genève 24, Suisse. E-Mail: [email protected]
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Abstract

Let φ be the Euler function, and consider the error term H in the asymptotic formula

MSC classification

Secondary: 11N64: Other results on the distribution of values or the characterization of arithmetic functions
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 161 - 164
Copyright
Copyright © University College London 2000

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References

1.Erdős, P. and Shapiro, H. M.. The existence of a distribution function for an error term related to the Euler function. Canad. J. Math., 7 (1955), 63–75.CrossRefGoogle Scholar
2.Lau, Y.-K.. Sign changes of error terms related to the Euler function. Mathematika (to appear).Google Scholar
3.Pétermann, Y.-F. S.. On the distribution of values of an error term related to the Euler function. Théorie des nombres (Québec, PQ, 1987), (de Gruyter, Berlin, 1989), 785–797.Google Scholar