# Mangoldt function

From Encyclopedia of Mathematics

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