= Homothety of complex lattices
{title2=$\Lambda'=a\Lambda$, $a\in\mathbb C^\times$}
= Homotheties of complex lattices
{synonym}
= Homothetic complex lattices
{synonym}
Two <complex lattices> are homothetic when multiplication by one nonzero complex number takes one onto the other. Changes between oriented integral bases have determinant one, so normalized period ratios classify these classes by $SL_2(\mathbb Z)\backslash\mathbb H$. The <lattice Eisenstein sums> scale as $G_k(a\Lambda)=a^{-k}G_k(\Lambda)$.
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