The Fundamental Theorem of Algebra and the Divergence of Reciprocals of Primes Looked at Through Bergman Spaces

TL;DR

This paper demonstrates how Bergman spaces can be used to prove fundamental facts in number theory, specifically relating to primes and their reciprocals.

Contribution

It introduces a novel approach by applying Bergman space theory to elementary number theory results involving primes.

Findings

Elementary number theory facts are proven using Bergman spaces.

The divergence of reciprocals of primes is analyzed through complex analysis.

New connections between number theory and functional analysis are established.

Abstract

Two well known facts from elementary number theory are proven by using Bergman spaces.