ScalingStacks

Proof. [042N]

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Proof.

This is the periodic version of Lemma 2.8, using Euler’s series identity for cot⁡(π​η)\cot(\pi\eta):

limN→∞∑n=−NN1η+n=π​cot⁡(π​η),\lim_{N\to\infty}\sum_{n=-N}^{N}\frac{1}{\eta+n}=\pi\cot(\pi\eta),

and ∑iβi​(0,0,1)=1\sum_{i}\beta_{i}(0,0,1)=1 from Lemma 2.8. ∎

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