Talk:Ramanujan's sum

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

$\int _{0}^{1}dxf(x)e^{inx}$

involved in circle method

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

Dirichlet g.f.

I think the 2nd formula under the generating function section should be written without the factor $n^{r}$ in the denominator. The Titchmarsh book Theory of the Riemann zeta-function shows only $\sigma _{1-r}(n)/\zeta (r)$. R. J. Mathar (talk) 16:34, 26 March 2011 (UTC)

I think both representations are correct. The article gives the function in terms of $\sigma _{r-1}(n)$, Titchmarsh in terms of $\sigma _{1-r}(n)$. The two are related but unequal, in general. Rwb001 (talk) 09:48, 24 August 2012 (UTC)

Table of values

I think the entries $c_{4}(12)$ to $c_{4}(20)$ 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 (talk • contribs) 09:14, 23 August 2012 (UTC)

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)

The pattern breaks down after $c_{4}(10)=-2$ (which is correct, I think). Then $c_{4}(12)$ is also given as -2. Should be +2, I think. Rwb001 (talk) 09:48, 24 August 2012 (UTC)

D'uh, you're right! I'll fix it. - Virginia-American (talk) 11:42, 24 August 2012 (UTC)

Looks OK now. Thanks! Rwb001 (talk) 08:05, 25 August 2012 (UTC)

Kluyver

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.