In this course, students will study the basic theory of elliptic
functions, or meromorphic functions which are "doubly periodic."
Although a seemingly innocuous definition, we will see that these
functions are connected to many of the important objects in modern
number theory, including elliptic curves, modular forms, and Jacobi
forms. No knowledge of elementary number theory is assumed, however
students should be familiar with complex analysis (Identity theorem,
Cauchy's theorem, etc.).
Lecture: Tuesday/Thursday, 4-5:30 PM in Seminarraum 1 des Mathematischen Instituts (Raum 005)
Exercise Sessions: Wednesday 10-11:30 AM in Seminarraum Weyertal 80/ Ecke Gyrhofstr., Institut für Informatik, UG links. With Dr. Michael Mertens.
Dr. Larry Rolen: Monday at 1 pm, unless otherwise stated here.
Dr. Michael Mertens: Thursday at 11 am, unless otherwise stated on his website.
M. Eichler, D. Zagier, The theory of Jacobi form, Progress in
Mathematics, 55. Birkhäuser Boston, Inc., Boston, MA, 1985. v+148 pp.
N. Koblitz, Introduction to elliptic curves and modular forms,
Second edition. Graduate Texts in Mathematics, 97. Springer-Verlag, New York, 1993. x+248 pp
M. Koecher und A. Krieg, Elliptische Funktionen und Modulformen, Springer-Lehrbuch Masterclass, 2007
Each Tuesday, a new homework sheet will be uploaded below, which is due
the following Tuesday and contains 4 questions, each of which is worth 4
points. Students are encouraged to discuss homework together, but you
must turn in your own work (i.e. no copying). The grade is based solely
on a final exam. However, in order to take the final, you must receive
at least a 50% score on homeworks, and you must present a homework
solution at least one time during the exercise sessions on Wednesdays.