https://en.wikipedia.org/wiki/P-adic_number

https://en.wikipedia.org/wiki/Ramanujan_summation

It is interesting, can this summation (1+2+3+4+5...=-1/12) be obtained in p-adic numbers?

6 hours ago, Linkey said:

It is interesting, can this summation (1+2+3+4+5...=-1/12) be obtained in p-adic numbers?

I think so, yes. Although (1+2+3+4+5...=-1/12) is usually considered in terms of the Riemann zeta function ζ(-1), it can also be obtained without explicit reference to the Riemann zeta function. I while ago, I derived this and other divergent series, and there seems to be a connection to the p-adic numbers.

Edited 7 hours ago7 hr by KJW

1 hour ago, KJW said:

I while ago, I derived this and other divergent series

If you're interested check out what I said in:

https://www.scienceforums.net/topic/131721-problem-with-cantor-diagonal-argument/page/6/#comments

which was a side discussion to the main topic of the thread.

I am sorry that I hurried and missed to write full name of the thread: "p-adic numbers and the Ramanujan summation". It seems that the thread name can not be modified by me now, can I ask moredators to modify it?

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