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Elementary remarks on Möbius’ function

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Abstract

Starting from identities obtained by Möbius inversion, we prove some inequalities involving the ordinary and logarithmic summatory functions of the Möbius function.

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References

  1. A. Axer, “Beitrag zur Kenntnis der zahlentheoretischen Funktionen μ(n) und λ(n),” Prace Mat.-Fyz. 21, 65–95 (1910).

    MATH  Google Scholar 

  2. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, 2nd ed. (Addison-Wesley, Reading, MA, 1994).

    MATH  Google Scholar 

  3. L. Kronecker, “Quelques remarques sur la détermination des valeurs moyennes,” C. R. Acad. Sci. Paris 103, 980–987 (1887).

    Google Scholar 

  4. E. Landau, “Über die Bedeutung einiger neuen Grenzwertsätze der Herren Hardy und Axer,” Prace Mat.-Fyz. 21, 97–177 (1910).

    MATH  Google Scholar 

  5. R. A. MacLeod, “A Curious Identity for the Möbius Function,” Util. Math. 46, 91–95 (1994).

    MathSciNet  MATH  Google Scholar 

  6. H. von Mangoldt, “Beweis der Gleichung \(\sum\nolimits_{k = 1}^\infty {\tfrac{{\mu (k)}} {k}} = 0\),” Sitzungsber. Kön. Preuss. Akad. Wiss., 835–852 (1897).

  7. E. Meissel, “Observationes quaedam in theoria numerorum,” J. Reine Angew. Math. 48, 301–316 (1854).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut de Mathématiques de Luminy, UMR 6206, CNRS, Université de la Méditerranée, Campus de Luminy, Case 907, 13288, Marseille Cedex 9, France

    Michel Balazard

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  1. Michel Balazard
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Correspondence to Michel Balazard.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Vol. 276, pp. 39–45.

To the memory of A.A. Karatsuba, on the occasion of his 75th anniversary

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Balazard, M. Elementary remarks on Möbius’ function. Proc. Steklov Inst. Math. 276, 33–39 (2012). https://doi.org/10.1134/S008154381201004X

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  • DOI: https://doi.org/10.1134/S008154381201004X

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