Abstract A formula connecting a moment of ‐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 ‐functions twisted by Dirichlet characters. This extends, via a new and simple argument, some results of Bettin, Drappeau, and Nordentoft.
Dasgupta et al. (Sun,) studied this question.