Talk:Ramanujan tau function

The sign of tau(n)?

Is there a simple criterion known when tau(n) is positive or negative? Ringspectrum (talk) 13:55, 4 September 2009 (UTC)

The multiplicative property will give some information on this. — Preceding unsigned comment added by 88.150.234.8 (talk) 08:13, 24 June 2014 (UTC)

Claimed proof of Lehmer's conjecture

A proof of Lehmer's 1947 conjecture, that τ is never zero, has been announced: Lee, Will Y. (16 Jun 2014). "Lehmer's Conjecture on the Non-vanishing of Ramanujan's Tau Function". arXiv:1406.3607 [math.NT].. Deltahedron (talk) 21:11, 16 June 2014 (UTC)

This paper contains major errors. The "proof" in Lemma 2 goes as follows: Step A: Assume equation (13). Step B: Do some computations. Step C: These computations lead to a contradiction; conclude that equation (13) is wrong. However, Step A was not used anywhere in Step B! The only logical conclusion is that there must be errors inside Step B (I checked (15) in an example and noticed that it is wrong for i=1,2,3,4). MvH (talk) 15:25, 22 August 2014 (UTC)MvH

Conjectures

The first paragraph under the heading "Conjectures on tau(n)" is rather odd. I think it comes from N. Lygeros and O. Rozier. — Preceding unsigned comment added by 88.150.234.8 (talk) 13:04, 23 June 2014 (UTC)

See User:Tsa1v.

The previous edit war, in 2011, in January and February, seems to be from the same parties. — Preceding unsigned comment added by Ice age 97 (talk • contribs) 13:35, 23 June 2014 (UTC)

The a(n) in the first paragraph might include tau(n) as a special case. — Preceding unsigned comment added by 88.150.234.8 (talk) 08:14, 24 June 2014 (UTC)

Dyson

The mentioned formula for tau was by Dyson and not by Macdonald, see the original article by Macdonald Inv. Math., 15, 1972, who attributed it to Dyson (or Dyson Missed opportunities)--Claude J (talk) 11:52, 21 September 2016 (UTC)

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Motivation?

Does anyone know what Ramanujan's motivation for studying this particular function was? It looks rather arbitrary to me (but that probably just means that I'm not that familiar with this field of mathematics). Where does the exponent 24 come from, for example?

Also, are there any uses for this function? Sometimes when I look at some works in mathematics, I'm wondering whether there is any practical application for those works at all, or whether the mathematicians simply did it all for their own (and other people's) pleasure. —Kri (talk) 23:06, 9 March 2023 (UTC)

Kri might study elliptic modular functions. — Preceding unsigned comment added by 2A00:23C4:7C8F:2B00:FD37:18CB:5181:71D2 (talk) 16:05, 3 April 2023 (UTC)

Priority

The title of this article mentions Ramanujan. The tau(n) function might have been mentioned earlier. 2A00:23C4:7C8F:2B00:FD37:18CB:5181:71D2 (talk) 16:11, 3 April 2023 (UTC)

I highly doubt it Nolord (talk) 10:05, 14 June 2026 (UTC)

Riemann hypothesis for the Ramanujan L-function

In the original manuscript from Ramanujan, I found no mention of a Riemann hypothesis for the L-function. I am not aware of any other work of him mentioning the tau function. A reference to the actual origin of the conjecture would be appreciated.

If it was first conjectured as part of a broader conjecture about L-functions, the article should be corrected accordingly. Nolord (talk) 10:11, 14 June 2026 (UTC)