Abstract
Let [Formula: see text] be a Dirichlet character. The main goal of this paper is to study oscillations of the difference [Formula: see text] where [Formula: see text] denotes the twisted Dedekind function. We prove that for infinitely many odd characters [Formula: see text] called “good”, we have [Formula: see text], and [Formula: see text] when [Formula: see text] is real. We give a necessary and sufficient condition for [Formula: see text] to be good, and in particular we prove that all odd primitive characters are good. We show also that there are infinitely many moduli [Formula: see text], including all prime powers [Formula: see text], for which all odd characters [Formula: see text] are good.
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