MATH-417 / 5 credits

Teacher(s): Lin Yongxiao, Raju Chandra Sekhar

Language: English


Summary

This year's topic is "Advanced Analytic Number Theory": this is a continuation of the course MATH-313 "Introduction to Analytic Number Theory". We will cover primes in arithmetic progressions, the Landau-Siegel zero, the Bombieri-Vinogradov Theorem and Vinogradov's three primes theorem (itp).

Content

Keywords

Primes numbers

Arithmetic progressions

L-functions and zero-free regions

The large Sieve

The circle method

Learning Prerequisites

Required courses

Analysis III & IV

Introduction to Analytic Number Theory.

 

Recommended courses

 

 

Important concepts to start the course

-Good knowledge of analysis in particular Fourier theory and theory of the complex variable.

Learning Outcomes

By the end of the course, the student must be able to:

  • Synthesize the analytic aspects of the theory of numbers
  • Solve advanced problems in analytic number theory

Transversal skills

  • Access and evaluate appropriate sources of information.
  • Make an oral presentation.
  • Demonstrate the capacity for critical thinking

Teaching methods

Ex-Cathedra Course

Expected student activities

We expect a proactive attitude during the courses and the exercises sessions (possibly with individual presentation of the solution of various problems).

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 a moodle with ressources for the course will be maintained

Resources

Bibliography

Davenport: Multiplicative Number Theory

Iwaniec-Kowalski: Analytic Number Theory

Ressources en bibliothèque

Prerequisite for

Current research in number theory

In the programs

  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Topics in 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: Topics in 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: Topics in number theory
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks

Reference week

 MoTuWeThFr
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