Liouville function
From Encyclopedia of Mathematics
The arithmetic function 
defined by
 |
where 
is the number of prime factors of 
. The Liouville function is closely connected with the Möbius function 
:
 |
In number theory an important estimate is that of the sum
 |
as 
. There is a conjecture that
 |
The most recent result, obtained by a method of I.M. Vinogradov, has the form
 |
The Liouville function was introduced by J. Liouville.
References
| [1] | K. Prachar, "Primzahlverteilung" , Springer (1957) |
| [2] | K. Chandrasekharan, "Arithmetical functions" , Springer (1970) |
How to Cite This Entry:
Liouville function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Liouville_function&oldid=44333
Liouville function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Liouville_function&oldid=44333
This article was adapted from an original article by A.F. Lavrik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article