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Representation of even Gaussian integer à la Chen

Soumyarup Banerjee, Habibur Rahaman

Abstract

In this article, we represent an even Gaussian integer with sufficiently large norm as a sum of a Gaussian prime and a Gaussian integer with at most two Gaussian prime factors akin to Chen in the rational case.

Representation of even Gaussian integer à la Chen

Abstract

In this article, we represent an even Gaussian integer with sufficiently large norm as a sum of a Gaussian prime and a Gaussian integer with at most two Gaussian prime factors akin to Chen in the rational case.

Paper Structure

This paper contains 9 sections, 25 theorems, 157 equations.

Table of Contents

  1. Introduction
  2. Background set up
  3. Lower bound of $r(\mathcal{N})$
  4. Linear Sieve in $\mathbb{Z}[i]$
  5. Lower bound of $S(\mathcal{A}, \mathcal{P}, z)$
  6. Upper bound for the average sum of $S(\mathcal{A}_\mathfrak{q}, \mathcal{P}, z)$
  7. Upper bound of $S(\mathcal{B},\mathcal{P},y)$
  8. Proof of Main Theorem
  9. Concluding Remarks

Key Result

Theorem \oldthetheorem

Let $\mathcal{N}$ be an even Gaussian integer. Then we have the lower bound where

Theorems & Definitions (45)

  • Theorem \oldthetheorem
  • Corollary \oldthetheorem
  • Lemma \oldthetheorem
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • Lemma \oldthetheorem
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • ...and 35 more