# Some arithmetic properties of an elliptic Dedekind sum

## TL;DR

This paper provides explicit formulas for elliptic Dedekind sums, explores their rational parts and zeros, and extends understanding of their arithmetic properties within the context of elliptic functions.

## Contribution

It offers a new explicit expression for elliptic Dedekind sums and analyzes their denominators and zeros, advancing the theoretical understanding of these sums.

## Key findings

- Explicit expression for elliptic Dedekind sum
- Determination of the denominator of the rational part
- Identification of zeros of the elliptic Dedekind sum

## Abstract

We give an explicit expression of the elliptic classical Dedekind sum which is a special case of multiple elliptic Dedekind sums introduced by Egami. We also determine the denominator of the rational part and zeros of the elliptic classical Dedekind sum.