#### Title of Research Output

#### Faculty

Science

#### Supervisor Name

Ajneet Dhillon

#### Keywords

math, pure math, number theory, complex analysis, prime numbers

#### Description

First proved by German mathematician Dirichlet in 1837, this important theorem states that for coprime integers a, m, there are an infinite number of primes p such that p = a (mod m). This is one of many extensions of Euclid’s theorem that there are infinitely many prime numbers. In this paper, we will formulate a rather elegant proof of Dirichlet’s theorem using ideas from complex analysis and group theory.

#### Acknowledgements

I would like to thank my supervisor Prof. Ajneet Dhillon for guiding me towards this topic for my summer research project. I thoroughly enjoyed the readings recommended and was able to deepen my understanding of pure math thanks to his time and effort. I also extend my thanks to Prof. Chris Kapulkin, who inspired me to pursue research opportunities and introduced me to the USRI program in 2021.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

#### Document Type

Paper

#### Included in

Proving Dirichlet's Theorem on Arithmetic Progressions

First proved by German mathematician Dirichlet in 1837, this important theorem states that for coprime integers a, m, there are an infinite number of primes p such that p = a (mod m). This is one of many extensions of Euclid’s theorem that there are infinitely many prime numbers. In this paper, we will formulate a rather elegant proof of Dirichlet’s theorem using ideas from complex analysis and group theory.