= Pole-subtracted theta integral for an Epstein zeta function
{title2=$\mathcal E_\Lambda(s)=A_\Lambda(s)+m^{-1}A_{\Lambda^\vee}(n/2-s)+m^{-1}/(s-n/2)-1/s$}
Put $a=n/2$, $m=m(\Lambda)$ and $A_\Lambda(s)=\int_1^\infty(\Theta_\Lambda(it)-1)t^{s-1}\,dt$, which is entire. Splitting the <Mellin transform> at one and using the <lattice theta functional equation> gives $\mathcal E_\Lambda(s)=A_\Lambda(s)+m^{-1}A_{\Lambda^\vee}(a-s)+m^{-1}/(s-a)-1/s$. The two rational terms explicitly retain the contributions of the zero lattice vector.
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