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For $s>0$, and $z\in\mathbb H=\{z=x+iy:y>0\}$, define $\theta(s;z)=\sum_{m,n\in\mathbb Z}e^{-\pi s\big(m^2y+\frac{(mx-n)^2}{y}\big)}$ and $ J(z;a,b)=\sum_{m,n\in\mathbb Z}e^{-\pi \big(m^2y+\frac{(mx-n)^2}{y}\big)} \cos\bigl(2\pi(ma+nb)\bigr)$ for the classical and shifted theta functions (Gaussian lattice sums), respec...
Let $\Th(\alpha,L)=\sum_{v\in L}e^{-\pi\alpha|v|^2}$ for $\alpha>0$ and $E(L,s)=\sum_{v\in L\setminus\{0\}}|v|^{-2s}$ for $s>3/2$ be the theta and Epstein zeta functions associated to the lattice $L$, respectively. We are particularly interested in physically relevant dimension three. Fix the covolume of the lattice $L...
Let the theta and Epstein zeta functions be $\Theta(\alpha,L)=\sum_{v\in L}e^{-\pi\alpha|v|^2}$ for $\alpha>0$ and $E(L,s)=\sum_{v\in L\setminus\{0\}}{|v|^{-2s}}$ for $s>2$, respectively. We consider full-rank lattices $L\subset\mathbb R^4$. Let the covolume of $L$ be one, and let $\mathcal D_4=2^{-1/4}D_4$ be the root...
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