# An average of generalized Dedekind sums

## TL;DR

This paper introduces a generalized Dedekind sum incorporating Dirichlet characters, derives its properties, computes its second moment explicitly via Fourier transform, and establishes bounds for this moment.

## Contribution

It presents a novel generalization of Dedekind sums with Dirichlet characters, including explicit formulas and bounds for their second moments.

## Key findings

- Explicit formula for the second moment of the generalized Dedekind sum
- Derived upper and lower bounds for the second moment
- Extended properties of classical Dedekind sums to a generalized setting

## Abstract

We study a generalization of the classical Dedekind sum that incorporates two Dirichlet characters and develop properties that generalize those of the classical Dedekind sum. By calculating the Fourier transform of this generalized Dedekind sum, we obtain an explicit formula for its second moment. Finally, we derive upper and lower bounds for the second moment with nearly identical orders of magnitude.