Lecture Notes on Sieve Methods

Lecture notes from my 2024 Dutch Mastermath course on Analytic Number Theory. I taught a 7-week module on sieve methods. The first 6 chapters (on prime number theory) can be found on Jan-Hendrik Evertse's webpage.


Chapter 7: Introduction to Sieves

Chapter 8: Brun's Pure Sieve

Chapter 9: Selberg's Sieve

Chapter 10: The Fundamental Lemma

Chapter 11: The Large Sieve

Chapter 12: Bounded Gaps Between Primes

Appendix: A Proof of the Bombieri-Vinogradov Theorem


These lecture notes were co-authored with my PhD student, Sebastián Carrillo Santana.