A Menon-type identity in residually finite Dedekind domains

A generalization of Menon-Rao-Sury's identities to additive characters by Tóth's method

“…Note that when s = 1, c 1 = 1 and F(a) = a, (1.8) reduces to (1.7) by µ * F = ϕ. For other related works on Menon's identity, see [2,3,7,8,10,12,13,[15][16][17][18] and references therein.…”