I'm trying to prove to myself that zeta(s) where s is a negative even number is 0 (the trivial zeroes of the Riemann zeta function), but I just get a positive number that's bigger with each term I add. Wtf.
This is not a troll. I figure I'm badly misinterpreting something, but I can't find what.
Like, for zeta(-2), that should be 1/1^-2 + 1/2^-2 + 1/3^-2 etc. i.e. 1/(1/[1*1]) + 1/(1/[2*2]) + 1/(1/[3*3]) etc. i.e. 1/(1/1) + 1/(1/4) + 1/(1/9) = 1+4+9. So what the fuck
Is there some other rule for the function on the domain from Re(s) { (-infinity, 1]?
This is not a troll. I figure I'm badly misinterpreting something, but I can't find what.
Like, for zeta(-2), that should be 1/1^-2 + 1/2^-2 + 1/3^-2 etc. i.e. 1/(1/[1*1]) + 1/(1/[2*2]) + 1/(1/[3*3]) etc. i.e. 1/(1/1) + 1/(1/4) + 1/(1/9) = 1+4+9. So what the fuck
Is there some other rule for the function on the domain from Re(s) { (-infinity, 1]?
