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Identities for series of the type $ \Sigma f(n)\mu (n)n\sp{-s}$


Author: Tom M. Apostol
Journal: Proc. Amer. Math. Soc. 40 (1973), 341-345
MSC: Primary 10A20; Secondary 10H15
MathSciNet review: 0319868
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Abstract: Identities are obtained relating the series of the title with $ \sum {f(n)\mu (n)\mu } (p,n){n^{ - s}}$ where $ f$ is completely multiplicative, $ \vert f(n)\vert \leqq 1$, and $ p$ is prime. Applications are given to vanishing subseries of $ \sum {\mu (n)/n} $.


References [Enhancements On Off] (What's this?)

  • [1] Tord Hall, Some relations in connection with the Möbius 𝜇-function, Nordisk Mat. Tidskr. 20 (1972), 34–36, 68 (Swedish, with English summary). MR 0337735
  • [2] J. C. Kluyver, Series derived from the series $ \sum {\mu (m)/m} $, Koningl. Akad. Wetensch. Amsterdam Proc. Sect. Sci. 6 (1904), 305-312.
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0319868-6
Keywords: Dirichlet series, Möbius function
Article copyright: © Copyright 1973 American Mathematical Society