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On the error-sum function of Pierce expansions

Min Woong Ahn

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.

On the error-sum function of Pierce expansions

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.
Paper Structure (4 sections, 9 theorems, 29 equations)

This paper contains 4 sections, 9 theorems, 29 equations.

Table of Contents

  1. Introduction
  2. Pierce expansion
  3. Some basic properties of $\mathcal{E}(x)$
  4. Symbolic space $\Sigma$

Key Result

Proposition 2.1

Let $x \in I$ and $n \in \mathbb{N}$. Then the following hold.

Theorems & Definitions (16)

  • Proposition 2.1: See Sha86 and Fan15
  • proof
  • Proposition 2.2: See Sha86
  • proof
  • Proposition 2.3: Fan15
  • Proposition 2.4
  • proof
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • ...and 6 more