Fundamental theorem of Algebra - A Nevanlinna theoretic proof

TL;DR

This paper presents a novel proof of the Fundamental Theorem of Algebra utilizing Nevanlinna theory, offering an alternative approach beyond traditional algebraic, analytical, and topological methods.

Contribution

It introduces a new proof of the Fundamental Theorem of Algebra based on Nevanlinna's value distribution theory, expanding the methods available for such proofs.

Findings

Proof using Nevanlinna's first fundamental theorem

Proof using Nevanlinna's second fundamental theorem

Demonstrates the applicability of complex analysis in algebraic proofs

Abstract

There are several proofs of the Fundamental Theorem of Algebra, mainly using algebra, analysis and topology. In this article, we have shown that the Fundamental Theorem of Algebra can be proved using Nevanlinna's first fundamental theorem as well as second fundamental theorem also.