Geodesic
Elementary remarks on M\"obius' function
Informatics and Automation, Number theory, algebra, and analysis, Tome 276 (2012), pp. 39-45.

Voir la notice de l'article provenant de la source Math-Net.Ru

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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Michel Balazard. Elementary remarks on M\"obius' function. Informatics and Automation, Number theory, algebra, and analysis, Tome 276 (2012), pp. 39-45. http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a3/

[1] Axer A., “Beitrag zur Kenntnis der zahlentheoretischen Funktionen $\mu (n)$ und $\lambda (n)$”, Prace mat.-fyz., 21 (1910), 65–95 | Zbl

[2] Graham R.L., Knuth D.E., Patashnik O., Concrete mathematics: A foundation for computer science, 2nd ed., Addison-Wesley, Reading, MA, 1994 | MR | Zbl

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

[4] Landau E., “Über die Bedeutung einiger neuen Grenzwertsätze der Herren Hardy und Axer”, Prace mat.-fyz., 21 (1910), 97–177 | Zbl

[5] MacLeod R.A., “A curious identity for the Möbius function”, Util. Math., 46 (1994), 91–95 | MR | Zbl

[6] von Mangoldt H., “Beweis der Gleichung $\sum _{k=1}^\infty \frac {\mu (k)}k =0$”, Sitzungsber. Kön. Preuss. Akad. Wiss., 1897, 835–852 | Zbl

[7] Meissel E., “Observationes quaedam in theoria numerorum”, J. reine angew. Math., 48 (1854), 301–316 | DOI | Zbl