Why are Ramanujan sums the same as the complex Zeta values?

[ddd123]

Possibly a difficult question, but I've never found a discussion on the topic.

Thanks

 

[ddd123]

Not much else to say, two examples:

1 + 2 + 3 + 4 + · · · = −1/12

1 + 1 + 1 + 1 + · · · = -1/2

This results both from Zeta regularization and Ramanujan summation. The two methods seem to me to be completely unrelated. It's an amazing coincidence so there must be a link between the two.

Another question would be: is it always true? But I'm assuming it is, or that the answer to the first question would answer this one too.

 

[ddd123]

Last attempt!

Thanks

 

[Strum]

Have you looked at this

http://mathoverflow.net/questions/6...ion-and-the-ramanujan-summation-how-strong-is