Rationality of Dedekind sums in function fields

In the previous paper we introduced the higher dimensional Dedekind sum in a function field (Bayad and Hamahata, Acta Arith. 152:71–80, 2012). The purpose of this paper is to present a criterion for the rationality of our Dedekind sum. To do so, we establish a connection between the field of definition of the Drinfeld module ϕ and the field of definition of the higher dimensional Dedekind sum sΛ(a0;a1,…,ad) associated to the A-lattice Λ, which corresponds to ϕ.