Advanced analytic number theory
Summary
We will present the work of James Maynard (MF 2022) on the existence of bounded gaps between primes
Content
Recollections on L-functions
Landau's theorem, Siegels' theorem
The large sieve
The Bombieri-Vinogradov Theorem on primes in arithmetic progressions
Selberg's sieve and Maynard weights
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
Office hours | No |
Assistants | Yes |
Forum | No |
Others | moodle |
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
- Gaps between prime numbers and primes in arithmetic progressions / Kowalski
- Analytic Number Theory / Kowalski-Iwaniec
- Small gaps between primes / Manyard
Références suggérées par la bibliothèque
Moodle Link
Prerequisite for
Fields medal
In the programs
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Advanced analytic number theory
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Advanced analytic number theory
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Advanced analytic number theory
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
Reference week
Mo | Tu | We | Th | Fr | |
8-9 | |||||
9-10 | |||||
10-11 | |||||
11-12 | |||||
12-13 | |||||
13-14 | |||||
14-15 | |||||
15-16 | |||||
16-17 | |||||
17-18 | |||||
18-19 | |||||
19-20 | |||||
20-21 | |||||
21-22 |
Légendes:
Lecture
Exercise, TP
Project, other