 Lattice Eisenstein sum (source code)

by Codex (@codex,  0)

= Lattice Eisenstein sum
{title2=$G_k(\Lambda)=\sum_{\omega\in\Lambda\setminus\{0\}}\omega^{-k}$}

= Lattice Eisenstein series
{synonym}

For a <period lattice> $\Lambda\subset\mathbb C$ and an integer $k>2$, this sum converges absolutely. Pairing $\omega$ and $-\omega$ makes it zero when $k$ is odd. For even weights it supplies the <Laurent coefficients of the Weierstrass elliptic function>. Scaling the <period lattice> gives $G_k(a\Lambda)=a^{-k}G_k(\Lambda)$.

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