On a unified theory of numbers

TL;DR

This paper presents a unified theoretical framework that connects various disparate results in number theory, such as divergent series, arithmetic functions, uniform distribution, and primes, enabling new insights and results.

Contribution

It introduces a single equation that unifies multiple areas of number theory, providing a novel approach to derive new results across these fields.

Findings

Unified framework for diverse number theory results

Derivation of new results in number theory using the unified approach

Connections established between previously independent number theory areas

Abstract

We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be independent results can be unified under a single equation. We apply our method to derive several new results in the above areas of number theory.