Values of Dedekind sums for function fields

Abstract

H. Rademacher and E. Grosswald raised the following questions: \begin{enumerate} \item Is $\{ (a/c, d(a,c))\ |\ a/c\in\mathbb{Q}^*\}$ dense in $\mathbb{R}^2$? \item Is $\{ d(a,c)\ |\ a/c\in\mathbb{Q}^*\}$ dense in $\mathbb{R}$? \end{enumerate} D. Hickerson answered them affirmatively, and H. Ito obtained a result similar to Hickerson's for the elliptic Dedekind sums defined by R. Sczech. We consider the values of the Dedekind sum attached to a given $A$-lattice in rational function fields. The objective of this paper is to establish a result similar to those of Hickerson and Ito.