Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On a Conjecture about Sums Involving Farey Fractions

Anji Dong, Xinyi Li, Vi Anh Nguyen

Abstract

In this paper, we prove a conjecture by Daniele Mundici on the sum of squared distances between consecutive elements in the $Q$-th Farey sequence for $Q\in\mathbb{Z}$ and $Q\geq 2$.

On a Conjecture about Sums Involving Farey Fractions

Abstract

In this paper, we prove a conjecture by Daniele Mundici on the sum of squared distances between consecutive elements in the -th Farey sequence for and .

Paper Structure

This paper contains 4 sections, 2 theorems, 54 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['thm: Theorem 2']}
  3. Proof of Theorem \ref{['thm: main theorem']}
  4. Some Open Problems

Key Result

Theorem 1.2

where $C(Q)$ is defined in def: C(n). $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (4)

  • Conjecture 1.1
  • Theorem 1.2
  • Theorem 1.3
  • proof