## Modular Forms (MAGIC049) |

## General## Description
Modular forms (and automorphic forms/representations) play an increasingly
central role in modern number theory, but also in other branches of mathematics
and even in physics. This course gives an introduction to the subject.
Here is a sample of topics we plan to cover:
- Modular curves, also as Riemann surfaces and as moduli space of elliptic
curves (over
**C**); - Modular functions and forms, basic properties, Eisenstein series, eta-function;
- Hecke operators, Petersson scalar product;
- Modular forms and Dirichlet series, functional equation;
- Theta series, arithmetic applications;
Prerequisites: Good command of complex analysis and algebra. Occasionally,
some knowledge of algebraic number theory and Riemann surface theory would be
helpful.
## SemesterSpring 2012 (Monday, January 16 to Friday, March 23) ## Timetable- Tue 15:05 - 15:55
## PrerequisitesGood command of complex analysis and algebra. Occasionally,
some knowledge of algebraic number theory and Riemann surface theory would be
helpful.
## SyllabusNo syllabus information is available yet.
## Students
## Bibliography
Note:
Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.) ## AssessmentThere will be two homework assignments which both need to be passed satisfactorily.
HW1: Due March 9
HW2: Due April 13
Assignment 1
Homework 2
## FilesFiles marked |