# On the error-sum function of Pierce expansions

## TL;DR

This paper introduces the error-sum function of Pierce expansions, analyzes its fundamental properties, and investigates its fractal nature through various dimensional measures.

## Contribution

It presents the first detailed study of the error-sum function for Pierce expansions, including its properties and fractal dimensions.

## Key findings

- The error-sum function exhibits fractal characteristics.
- The Hausdorff, box-counting, and covering dimensions of its graph are calculated.
- Basic properties of the error-sum function are established.

## Abstract

We introduce the error-sum function of Pierce expansions. Some basic properties of the error-sum function are analyzed. We also examine the fractal property of the graph of it by calculating the Hausdorff dimension, the box-counting dimension, and the covering dimension of the graph.