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On elementary estimates for the partition function

Mizuki Akeno

Abstract

In this paper, we obtain upper and lower bounds for the partition function $p(n)$ by using an elementary geometric inequality in Euclidean space, and we extend the method to generalizations of the partition function.

On elementary estimates for the partition function

Abstract

In this paper, we obtain upper and lower bounds for the partition function by using an elementary geometric inequality in Euclidean space, and we extend the method to generalizations of the partition function.

Paper Structure

This paper contains 8 sections, 11 theorems, 135 equations.

Table of Contents

  1. Introduction
  2. Bounds for partition function
  3. Sum of the partition function
  4. Framework
  5. Partition function
  6. Preliminaries
  7. Generalization 1
  8. Generalization 2

Key Result

Theorem 1

For all $N \in \mathbb{Z}_{\geq 1}$, we have

Theorems & Definitions (21)

  • Theorem 1
  • proof : Proof of Theorem \ref{['P1']}
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 2
  • proof
  • Lemma 3
  • Lemma 4
  • ...and 11 more