kevin lucas on Fri, 15 Feb 2019 18:28:51 +0100

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Evaluating Multiple Sums in PARI/GP

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.