On the Asymptotic Behavior of Dedekind Sums
Institut für Mathematik
Let z be a real quadratic irrational. We compare the asymptotic
behavior of Dedekind sums S(pk,
qk) belonging to convergents
of the regular continued fraction expansion of z with
that of Dedekind sums
belonging to convergents
of the negative regular continued fraction expansion of z.
Whereas the three main cases of this behavior are closely related, a
more detailed study of the most interesting case (in which the Dedekind
sums remain bounded) exhibits some marked differences, since the
cluster points depend on the respective periods of these expansions.
We show in which cases cluster points of
can coincide with
cluster points of
An important tool for our purpose is a
criterion that says which convergents
of z are convergents
Full version: pdf,
Received March 14 2014;
revised version received July 3 2014.
Published in Journal of Integer Sequences, July 11 2014.
Journal of Integer Sequences home page