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s− 1) + 8s−1 2·6s ζ(3s)−R24,p,2(s)
2 3
3
√ 3 4 · x 2
3
16, p, 1 ζ(s)ζ(2s)− 1 2s−1ζ(3s− 1)− ζ(3s) +R16,p(s) 1 ζ(2)x
16, p, 2 1 2s−1ζ(3s− 1)−R16,p(s)
2 3
3 2 · x 2
3
16, i, 1 1 4s(s−1)ζ(3s− 1)−R16,i,1(s) [...] ζ(s)3 = 6FG8,p(s) + 3FG16,p,1(s) + 3FG16,p,2(s) + FG48,p(s) .
Taking into account the results that we have already established for the primitive tetragonal and cubic cases, we conclude
FG8,p(s) = ζ(s)3
6 [...] with
g(1) = lim s→1 σ>1
(s− 1)F16,p,1(s) = ζ(2) .
With the Theorem of Delange we see that
fG16,p,1(x) = ζ(2)x .
50
G16,p,2 We start with
F16,p,2(s) = 1
2s− 1 ζ(3s− 1)−R16,p(s) .
The rightmost singularity …