A generalization of a Menon-type identity by Tóth in residually finite Dedekind domains

In this paper, we further investigate Dirichlet characters and additive characters in the field of residually finite Dedekind domains. We present a novel variant of T & oacute;th's identity, specifically, a Menon-type identity for arithmetic functions involving both Dirichlet characters and additive characters in residually finite Dedekind domains. It can be viewed as an extension of Chen and Zheng's identity (2022). As an application, we provide a version of the Menon-type identity in the ring of integers of a number field.