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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the order of some error functions related to $k$-free integers
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by V. S. Joshi
Proc. Amer. Math. Soc. 35 (1972), 325-332
DOI: https://doi.org/10.1090/S0002-9939-1972-0337839-X

Erratum: Proc. Amer. Math. Soc. 51 (1975), 251-252.

Abstract:

Let ${\Delta _k}(x)$ and $\Delta {’_k}(x)$ be the error functions in the asymptotic formulae for the number and the sum of k-free integers not exceeding x. We prove that on the assumption of Riemann hypothesis, we have \[ \Delta {’_k}(x) - x{\Delta _k}(x) = O({x^{1 + 1/2k + \varepsilon }})\] and \[ \frac {1}{x}\int _1^x {{\Delta _k}(t)dt = O({x^{1/2k + \varepsilon }}),} \] for arbitrary $\varepsilon > 0$.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 325-332
  • MSC: Primary 10H25
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0337839-X
  • MathSciNet review: 0337839