TITLE: contradictory wikipedia and mathworld.wolfram
QUESTION [8 upvotes]: On https://en.wikipedia.org/wiki/Liouville_function there is written $L(n)>0.06 \sqrt n$ and $L(n)<-1.39 \sqrt(n)$ for infinitely many $n$.
On http://mathworld.wolfram.com/LiouvilleFunction.html they say it is unknown if $L(n)$ changes sign infinitely many times.
But those statements are contradicting each other. 
(so one has to contact that site which is wrong)
So which one of the statements is true?

REPLY [2 votes]: I found no evidence that $L(n) < 0$ for infinitely many $n$.  But maybe I just missed it.  I checked the relevant reference, which can be found here as of the time I write this - http://www.ams.org/journals/mcom/2008-77-263/S0025-5718-08-02036-X/
Click on "Full-text PDF" to read it.
Near the top of page 1685 it says, "...With this information, the method of Anderson and Stark shows that
$$ L(n) > 0.027536\sqrt{n}$$
infinitely often."
Near the middle-bottom of page 1693 (just before the acknowledgments) it says, "With this computation, we verified that indeed $L(n) < 0$ for $10^9 \le n \le 2 \cdot 10^{14}$."  I think that's the best they did in terms of when $L(n) < 0$.