'Modular Forms'
(Mastercollege Modulaire Vormen)
This course intends to give an introduction to the area of
modular forms.
Modular forms occurs every where in mathematics,
in algebraic geometry, in number theory and even in
string theory. They play a very important role, for
example they were pivotal for the proof of Wiles
of Fermats Last Theorem.
Prerequisites are a (modest) knowledge of
algebra and function theory. Some knowledge of algebraic
geometry and number theory will be helpful, but is not absolutely necessary.
Topics treated are: modular forms on SL(2,Z), Hecke operators,
modular symbols, Atkin-Lehner theory, periods, Dirichlet series,
modular curves, Eichler-Shimura, Galois representations and
Siegel modular forms.
Literature:
F. Diamond, J. Shurman: A first course in modular forms.
Graduate Texts in Math 228, Springer Verlag 2005.
W. Stein: Modular Forms, a computational approach. Graduate Studies
in Math. AMS 2007.
G. Shimura: Introduction to the arithmetic theory of automorphic
functions. Princeton University Press.
J. Bruinier, G. van der Geer, G. Harder, D. Zagier: The 1-2-3 of Modular Forms. Springer Verlag, 2008.
More references to the literature will be given during the course.
The course starts in week 36 of 2011.
Time: Thursday 11:00-12:45
Location: Nikhef F 2.19 (till including October 27), starting November 3
in room Nikhef F 2.21, Science Park 105, see here
Here are the exercises-1
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