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sum 1/(m^3+n^3)
Posted:
Jun 19, 1996 3:47 PM


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 jriccio@mit.edu
James Riccio jriccio@mit.edu "The following statement is true." "The precedeing statement is false."



