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The Theory of ramification

Theophilus Agama

Abstract

In this paper, we introduce and develop the concept of \emph{ramification} in a given modulus. We study some properties in relation to this concept and it's connection to some important problems in mathematics, particularly the Goldbach conjecture.

The Theory of ramification

Abstract

In this paper, we introduce and develop the concept of \emph{ramification} in a given modulus. We study some properties in relation to this concept and it's connection to some important problems in mathematics, particularly the Goldbach conjecture.

Paper Structure

This paper contains 8 sections, 13 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Organization of the paper
  3. The concept of ramification
  4. Properties of the ramifier
  5. The index of ramification
  6. The circle of ramification
  7. Ramification character
  8. Final remarks

Key Result

Proposition 3.1

There exist a ramifier in a fixed modulus. In particular, for any $m\geq 2$, there exists a ramifier in $\pmod t$ for a fixed $1<t\leq m$.

Theorems & Definitions (42)

  • Definition 2.1
  • Remark 2.2
  • Proposition 3.1
  • proof
  • Remark 3.2
  • Proposition 3.3
  • proof
  • Theorem 3.4
  • proof
  • Remark 3.5
  • ...and 32 more