Advanced analytic number theory

Summary

We will present the work of James Maynard (MF 2022) on the existence of bounded gaps between primes

Content

Keywords

zeta and L-functions

Learning Prerequisites

Required courses

MATH-100

MATH-105

MATH-200

MATH-313

Recommended courses

MATH-337

Learning Outcomes

• Quote the main results of the course
• Use the main results of the course
• Prove the main results of the course

Teaching methods

Ex cathedra lecture and exercises in the classroom

Expected student activities

Attendence to the lectures and active participation to thhe exercise sessions

Assessment methods

Oral exam

====================
Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux
étudiants concernés.

Supervision

Resources

Bibliography

Kowalski, Emmanuel Gaps between prime numbers and primes in arithmetic progressions [after Y. Zhang and J. Maynard]. Astérisque No. 367-368 (2015), Exp. No. 1084

Kowalski-Iwaniec: Analytic Number Theory

James Maynard: Small gaps between primes. Ann. of Math. (2) 181 (2015)

Maynard James: Lateralus

Ressources en bibliothèque

• Small gaps between primes / Manyard
• Gaps between prime numbers and primes in arithmetic progressions / Kowalski
• Analytic Number Theory / Kowalski-Iwaniec

Références suggérées par la bibliothèque

• Lateralus / Maynard (Tool) : page wikipedia

Moodle Link

• https://go.epfl.ch/MATH-521

Prerequisite for

Fields medal