, Volume 30, Issue 3, pp 437-441
Date: 19 Sep 2012

Rationality of Dedekind sums in function fields

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

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 s Λ (a 0;a 1,…,a d ) associated to the A-lattice Λ, which corresponds to ϕ.