Number theory II.b - Modular forms
Summary
In this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization.
Content
During the course we will learn:
- Basic definitions and facts of the theory of modular forms
- Combinatorial properties of the Fourier expansions of modular forms
- Applications of modular forms to harmonic analysis
- Modular forms and the sphere packing problem
Keywords
Modular forms, Modular group, linear frantional transformations, theta functions.
Learning Prerequisites
Required courses
Recommended courses
Required courses
Complex analysis
Fourier analysis
Recommended courses
Algebraic topology
Riemann surfaces.
Assessment methods
Weekly graded homeworks and oral exam
Resources
Bibliography
Bibliography
- A first course in modular forms. Fred Diamond; Jerry Shurman; 2005
- The 1-2-3 of modular forms : lectures at a summer school in Nordfjordeid, Norway. Don Zagier; 2008
- Topics in Classical Automorphis forms. Henryc Iwaniec
Ressources en bibliothèque
Moodle Link
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Number theory II.b - Modular forms
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Number theory II.b - Modular forms
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Number theory II.b - Modular forms
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
Semaine de référence
| Lu | Ma | Me | Je | Ve | |
| 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:
Cours
Exercice, TP
Projet, Labo, autre