Advanced analytic number theory

MATH-521 / 5 credits

Teacher:

Language: English

Remark: pas donné en 2024-25. Cours donné en alternance tous les deux ans

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

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
  • Type: optional
  • 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
  • Type: optional
  • 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
  • Type: optional

Reference week

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