The density of the graph of elliptic Dedekind sums

TL;DR

This paper proves that the graph of normalized elliptic Dedekind sums is dense in its image across all imaginary quadratic fields, extending previous Euclidean case results, and explores properties of Martin's continued fraction algorithm.

Contribution

It generalizes Ito's density result from Euclidean to all imaginary quadratic fields and analyzes Martin's continued fraction algorithm in this broader context.

Findings

Density of the graph in all imaginary quadratic fields.

Basic properties of Martin's continued fraction algorithm.

Extension of Euclidean case results to a broader class of fields.

Abstract

We show that the graph of normalized elliptic Dedekind sums is dense in its image for arbitrary imaginary quadratic fields, generalizing a result of Ito in the Euclidean case. We also derive some basic properties of Martin's continued fraction algorithm for arbitrary imaginary quadratic fields.