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.
In the article above, denotes the Möbius function.
|[a1]||G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Oxford Univ. Press (1979) pp. Sect. 17.7|
Mangoldt function. S.A. Stepanov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Mangoldt_function&oldid=14110