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Mangoldt function

From Encyclopedia of Mathematics
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The arithmetic function defined by

The function has the following properties:

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 :

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. S.A. Stepanov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Mangoldt_function&oldid=14110
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098