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

  1. Feb 20, 2015 #1
    Possibly a difficult question, but I've never found a discussion on the topic.

    Thanks
     
  2. jcsd
  3. Feb 25, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Mar 1, 2015 #3
    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.
     
  5. Mar 15, 2015 #4
    Last attempt!

    Thanks
     
  6. Mar 16, 2015 #5
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