The residue of \(\zeta_G(s)\) at \(s=0\) is a value \(C\). I think I need to fuck with this more. And just run the sum and calculate the residue. Which will give us what to look for:
\[
\zeta_G(s) - \frac{C}{s} \,\,\text{is holomorphic at}\,\, s = 0\\
\]
The manner I've taken so far has solely been able to bound \(a \le C \le b\)............... but with some decent accuracy
\[
\zeta_G(s) - \frac{C}{s} \,\,\text{is holomorphic at}\,\, s = 0\\
\]
The manner I've taken so far has solely been able to bound \(a \le C \le b\)............... but with some decent accuracy

