Reciprocity for The Short Twisted Second Moment of The Riemann Zeta Function

Ze Sen Tang

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arXiv · 2608.14852

Reciprocity for The Short Twisted Second Moment of The Riemann Zeta Function

Ze Sen Tang

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Abstract

We prove a reciprocity formula for a twisted second moment of the Riemann zeta function over a short interval of length $T^{\delta}$, where $\delta \in (\frac{1}{2},1)$, centered at height $T$ on the critical line. This result extends Khan's reciprocity formula to the short interval setting and makes explicit the relation between the twisting parameters and the interval length.

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Ze Sen Tang. 2026-08-14. Reciprocity for The Short Twisted Second Moment of The Riemann Zeta Function. https://arxiv.org/abs/2608.14852

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