Talk:Ramanujan's sum

Latest comment: 12 years ago by Rwb001 in topic Table of values

Although i can not be 100 % sure, i think Ramanujan sum is also related to circle method to evaluate (n--> oo) the integrals:

involved in circle method

--85.85.100.144 18:34, 30 October 2007 (UTC)Reply

Dirichlet g.f.

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I think the 2nd formula under the generating function section should be written without the factor   in the denominator. The Titchmarsh book Theory of the Riemann zeta-function shows only  . R. J. Mathar (talk) 16:34, 26 March 2011 (UTC)Reply

I think both representations are correct. The article gives the function in terms of  , Titchmarsh in terms of  . The two are related but unequal, in general. Rwb001 (talk) 09:48, 24 August 2012 (UTC)Reply

Table of values

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I think the entries   to   may have the incorrect signs. Note for instance that the 4th row of the table does not have period 4, as I think it should. — Preceding unsigned comment added by Rwb001 (talkcontribs) 09:14, 23 August 2012 (UTC)Reply

Eh? row 4 is 0,-2,0,2, over and over. Compare to rows 8 and 16 - Virginia-American (talk) 22:24, 23 August 2012 (UTC)Reply
The pattern breaks down after   (which is correct, I think). Then   is also given as -2. Should be +2, I think. Rwb001 (talk) 09:48, 24 August 2012 (UTC)Reply
D'uh, you're right! I'll fix it. - Virginia-American (talk) 11:42, 24 August 2012 (UTC)Reply
Looks OK now. Thanks! Rwb001 (talk) 08:05, 25 August 2012 (UTC)Reply

Kluyver

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Jan Cornelis Kluyver seems to be the one in the article.

Kluyver wrote in 1906. I am not sure that the sums were introduced by Ramanujan.
Ramanujan said that a "few" of the properties had been mentioned earlier. He was probably referring to Kluyver.