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Topic: sum 1/(m^3+n^3)
Replies: 2   Last Post: Jun 19, 1996 11:28 PM

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James P Riccio

Posts: 1
Registered: 12/12/04
sum 1/(m^3+n^3)
Posted: Jun 19, 1996 3:47 PM
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Okay, here's what up. I considered the problem

sum(m=1..infinity,n=1..infinity) of 1/(m^2+n^2). Actually,
a friend of mine thought of that, and then gave it to me. I proved
it divereged fairly quickly. Then I showed that by replace the 2 with
and x>2, it converges, and I found nice bounds for the limit. Then I
extened it to three dimensions, then to n dimensions. In each case,
if the exponent is less than or equal to the number of dimensions, it
diverges, otherwise it converges (real exponents only, obviously).
This is in accord with the Riemann zeta function (which is this sum
with one dimension), i.e. zeta(1)=infinity, zeta(1+x)<infinity, x>0.
My question is, where can I find a good article about this particular subject.
I would like to see what bounds others have come up with, and so on.
If you could tell me which journal, issue, etc., or book it's in, I'd
be most appreciative. Email me at

James Riccio
"The following statement is true."
"The precedeing statement is false."

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