The Limiting Distribution of Elliptic Dedekind Sums

TL;DR

This paper proves that elliptic Dedekind sums, as generalizations of classical sums to complex lattices, follow a Gaussian distribution when suitably normalized, and confirms a related conjecture by Ito.

Contribution

It establishes the Gaussian limiting distribution of elliptic Dedekind sums and verifies a conjecture by Ito, extending classical results to complex lattices.

Findings

Elliptic Dedekind sums have a Gaussian limiting distribution.

The paper confirms Ito's conjecture regarding these sums.

Normalization is key to observing the distribution.

Abstract

We consider elliptic Dedekind sums that were introduced by Sczech as generalizations of the classical ones to complex lattices. We prove that these sums -- suitably normalized -- have a Gaussian limiting distribution. As an application, we prove a conjecture due to Ito.