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Solutions to some sign change problems on the functions involving sums of divisors

Yuchen Ding, Hao Pan, Yu--Chen Sun

Abstract

In this note, we solve some sign change problems on the functions involving sums of divisors posed by Pongsriiam recently.

Solutions to some sign change problems on the functions involving sums of divisors

Abstract

In this note, we solve some sign change problems on the functions involving sums of divisors posed by Pongsriiam recently.
Paper Structure (4 sections, 7 theorems, 51 equations)

This paper contains 4 sections, 7 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['thm1']}
  3. Proof of Theorem \ref{['thm2']}
  4. Proof of Theorem \ref{['thm3']}

Key Result

Theorem 1.1

The answer to Problem problem1 is negative.

Theorems & Definitions (12)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Lemma 2.1: Dirichlet
  • proof : Proof of Theorem \ref{['thm1']}
  • Lemma 3.1
  • proof : Proof of Theorem \ref{['thm2']}
  • Theorem 4.1
  • Lemma 4.1: Heath--Brown
  • proof : Proof of Theorem \ref{['thm4']}
  • ...and 2 more