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.).
Location/Times
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.
Office Hours
Dr. Larry Rolen: Monday at 1 pm, unless otherwise stated here.
Dr. Michael Mertens: Thursday at 11 am, unless otherwise stated on his website.
Literature
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
Course Policy
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.
