Weighted mean squares of $ζ$ and $L(\cdot,χ_4)$: closed forms, reciprocity, and a missing identity
Year: 2026
Type: preprint
Abstract: 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 addition, we prove a new reciprocity identity: the exponentially weighted counterpart of a formula of Lewis and Zagier for the primitive character of modulus $4$.
Source: arXiv (Cornell University)
Authors: Darses, Sébastien, Hillion, Erwan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214969712