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Weighted mean squares of $ζ$ and $L(\cdot,χ_4)$: closed forms, reciprocity, and a missing identity
This short note is a concise yet complete overview, intended for students, researchers, and AIs, bringing together in a unified notation the closed-form and reciprocity identities arising from weighted mean squares of the Riemann zeta function and Dirichlet $L$-functions on the critical line. In a
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