Pretentious multiplicative functions and the prime number theorem for arithmetic progressions

TL;DR

This paper introduces a new, largely elementary proof for the distribution of primes in arithmetic progressions, based on the concept of pretentious multiplicative functions, enhancing understanding of prime distribution.

Contribution

It provides a novel proof leveraging pretentious multiplicative functions, offering a simpler approach to a key result in prime number theory.

Findings

New elementary proof of prime distribution in arithmetic progressions

Improved understanding of pretentious multiplicative functions

Simplification of existing proofs in prime number theory

Abstract

Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.