Mangoldt function
From Encyclopedia of Mathematics
The arithmetic function defined by
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The function has the following properties:
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where the sums are taken over all divisors of
. The Mangoldt function is closely connected with the Riemann zeta-function
. In fact, the generating series for
is the logarithmic derivative of
:
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The Mangoldt function was proposed by H. Mangoldt in 1894.
Comments
In the article above, denotes the Möbius function.
References
[a1] | G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Oxford Univ. Press (1979) pp. Sect. 17.7 |
How to Cite This Entry:
Mangoldt function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mangoldt_function&oldid=14110
Mangoldt function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mangoldt_function&oldid=14110
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article