Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Proof.
Applying Lemma 5.3
(5.42) 𝒲 ( 𝒢 k ( z ) , 𝒟 k ( z ) ) = − z ⋅ n ( λ k n ) 1 2 ⋅ z n 2 − 1 ⋅ 1 2 ( λ k n ) 1 2 z n 2 = − n 2 . \mathcal{W}(\mathcal{G}_{k}(z),\mathcal{D}_{k}(z))=-z\cdot n(\frac{\lambda_{k}}{n})^{\frac{1}{2}}\cdot z^{\frac{n}{2}-1}\cdot\frac{1}{2(\frac{\lambda_{k}}{n})^{\frac{1}{2}}z^{\frac{n}{2}}}=-\frac{n}{2}.