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On the Order of the Error Function of the (k, r)-Integers—II

Published online by Cambridge University Press:  20 November 2018

M. V. Subbarao  and
D. Suryanarayana
M. V. Subbarao
Affiliation:
University of Alberta, Andhra University, University of Toledo and University of Georgia
D. Suryanarayana
Affiliation:
University of Alberta, Andhra University, University of Toledo and University of Georgia
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Abstract

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In the first part of this note we give a very simple and elegant proof of the theorem on the order of the error function of the (k, r)-integers, which the authors proved earlier using elaborate calculations. We also obtain an improvement of an earlier result on the order of the same error function on the basis of the Riemann hypothesis.

Keywords

10A20r-free integersRiemann hypothesisRiemann zeta functionMöbius function
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 3 , 01 September 1977 , pp. 397 - 399
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Axer, A., Über einige Grenzwertsätze, S.B. Akad. Wiss. Wien (2a), 120 (1911), 1253-1298.Google Scholar
2. Suryanarayana, D. and Sitaramachandra Rao, R., On the order of the error function of the k-free integers, Proc. Amer. Math. Soc. 28 (1971), 53-58.Google Scholar
3. Suryanarayana, D. and Sitaramachandra Rao, R., Uniform 0-estimate for k-free integers, J. Reine Angew. Math. 261 (1973), 146-152.Google Scholar
4. Subbarao, M. V. and Suryanarayana, D., On the order of the error function of the (k, r)-integers, J. Number Theory, 6 (1974), 112-123.Google Scholar
5. Walfisz, A., Weylsche Exponentialsumman in der neueren Zahlentheorie, Mathematische Forschungsberichte, 15, VEB Deutscher Verlag, Berlin, 1963.Google Scholar