arXiv subjects
Publications and source records attributed to Ze Sen Tang.
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.
A formula connecting a moment of L-functions and a dual moment in a way that interchanges the roles of certain key parameters on both sides is known as a reciprocity relation. We establish a reciprocity relation for a first moment of GL(2) L-functions twisted by Dirichlet characters. This extends, via a new and simple argument, some results of Bettin, Drappeau, and Nordentoft.
We give a new proof of Heath-Brown's full asymptotic expansion for the second moment of Dirichlet L-functions and we obtain a corresponding asymptotic expansion for a twisted first moment of Hecke-Maass L-functions.