I recently ran into problems attempting to formulate a PARI program that evaluated the _expression_
sum(((-1)^(a+b+c))/(a^2 + b^2 + c^2)^s)
for various complex values of s, with a,b,c running over Z^3/{(0,0,0)}. How should I attempt this? More generally, how should one set up iterated alternating sums like these? If, for instance I also wanted the eight-dimensional version of the above sum, how would I compute it?
As always any help and especially references are welcome.
Kevin