Generalization of Bertrand's Postulate for Gaussian Primes
Number Theory
2024-09-09 v3
Abstract
Bertrand's Postulate states about the prime distribution for the real numbers. The generalization of Bertrand's Postulate was proved by Das et al. [Arxiv 2018]. In this paper, we have formalized this idea for the Gaussian primes (or the primes on the complex plane). This result gives information about the prime distribution on the complex plane.
Cite
@article{arxiv.1901.07086,
title = {Generalization of Bertrand's Postulate for Gaussian Primes},
author = {Madhuparna Das},
journal= {arXiv preprint arXiv:1901.07086},
year = {2024}
}
Comments
The claim of Main Theorem 1 is wrong. The prime counting function on the complex plan does not satisfy the inequality. The prime number Theorem contradicts the claim