Modular Forms (MAGIC049) |
GeneralDescription
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:
Prerequisites: Good command of complex analysis and algebra. Occasionally, some knowledge of algebraic number theory and Riemann surface theory would be helpful. SemesterAutumn 2016 (Monday, October 3 to Friday, December 9) Timetable
PrerequisitesGood command of complex analysis and algebra. Occasionally,
some knowledge of algebraic number theory and Riemann surface theory would be
helpful.
Syllabus(1) Modular curves, also as Riemann surfaces and as moduli space of elliptic curves (over C) (2) Modular functions and forms, basic properties, Eisenstein series, eta-function (3) Theta series, arithmetic applications (4) Modular forms and Dirichlet series, functional equation (5) Hecke operators, Petersson scalar product 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.) AssessmentThe assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. There will be questions worth 100 marks and you will need 50 marks to pass.
FilesFiles marked L are intended to be displayed on the main screen during lectures.
Recorded LecturesPlease log in to view lecture recordings. |