Dedekind sums, function fields
Dedekind used the classical Dedekind sum
$D(a,c)$ to describe
the transformation of $\log\eta (z)$ under
the substitution $z'=(az+b)/(cz+d)$,
$\begin{pmatrix}a & b\\ c & d\end{pmatrix}\in
SL_2(\mathbb{Z})$.
In this paper,
we use the Dedekind sum $s(a,c)$ in function fields
to describe the transformation of a certain series under
the substitution $z'=(az+b)/(cz+d)$,
$\begin{pmatrix}a & b\\ c & d\end{pmatrix}\in
GL_2(\mathbb{F}_q[T])$.
Dedekind sums and the transformation formula in function fields
Research papers (academic journals)
