Reciprocity and the Kernel of Dedekind Sums
Alexis LaBelle, Emily Van Bergeyk, Matthew P. Young
TL;DR
This paper explores symmetries in Dedekind sums derived from Atkin-Lehner operators to analyze their kernel, introducing a new family of reciprocity formulas.
Contribution
It introduces a novel family of reciprocity formulas for newform Dedekind sums using Atkin-Lehner operators, aiding in understanding their kernel.
Findings
Generated a family of reciprocity formulas for Dedekind sums.
Identified symmetries that help analyze the kernel of Dedekind sums.
Provided new insights into the structure of Dedekind sums.
Abstract
We use the action of Atkin-Lehner operators to generate a family of reciprocity formulas for newform Dedekind sums. This family of reciprocity formulas provides symmetries which we use to investigate the kernel of these Dedekind sums.
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