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.