Talk:Liouville function

anon edits

changed the last formula slightly(lambda(s) is actually lambda(n) ) and added 2 comments (unsigned, undated)

Conjecture attribution

One of our more capable anonymous users changed attribution of the positivity conjecture to mention Paul Turan, removing attirubtion to Polya. Are there cites/references for this? The change is in direct contradition to mathworld, see Polya Conjecture, which states: The conjecture was made in 1919, and disproven by Haselgrove (1958) and cites Haselgrove, C. B. "A Disproof of a Conjecture of Pólya." Mathematika 5, 141-145, 1958., so it would seem that Haselgrove thought it was Polya's conjecture ... linas 21:58, 19 August 2005 (UTC)[reply]

Oh, never mind. I can't read. There are two conjectures on this page, one is Polya's and one whose origins are vague. linas 22:03, 19 August 2005 (UTC)[reply]

Infinitely many sign changes?

Back in 2010, an IP edit inserted

 It has since been shown that L(n) > 0.0618672√n for infinitely many positive integers n, while it can also be shown that L(n) < -1.3892783√n for infinitely many positive integers n.

but with a (valid) reference only for the first part. The referenced paper by Borwein et al. does not seem to have anything related to the second claim, and other sources (such as MathWorld) still, after almost six years, say that it is unknown whether infinitely many sign changes occur (whereas this question would be answered positively if the above claim were correct). I'll tentatively add a "citation needed", but am afraid the claim should in fact rather be dropped.--Hagman (talk) 13:07, 1 April 2016 (UTC)[reply]

ambiguous notation

The article mix Dirichlet power with term-by-term power, in the formula

The Dirichlet inverse of Liouville function is the absolute value of the Möbius function, \lambda ^{-1}(n)=|\mu (n)|=\mu ^{2}(n),

(\lambda ^{-1} is is Dirichlet power, while \mu ^{2} is a term by term power) 2A01:E0A:9D1:7200:D3FF:6D19:95C6:5618 (talk) 20:14, 29 November 2021 (UTC)[reply]