Modular Forms Spring 2019

Information

Lecturer

Prof. Dr. Özlem Imamoglu

Coordinator

Alessandro Lägeler

Room

LFV E41

Time

15:15-17:00

Schedule

Each student is expected to lecture on one of the subjects listed below. On the first week, we will distribute the subjects among the participants. The first and second week, Prof. Imamoglu will give an overview of the subject. The talks will start on the third week.  

Date	Talk	Speakers
20th February 2019	Overview and distribution of the talks	Imamoglu
27th February 2019	Historical overview	Imamoglu
6th March 2019	The modular group and the fundamental domain	Johannes, Manuel
13th March 2019	Definition of modular forms and first examples	Etienne, Aurel
20th March 2019	No class
27th March 2019	The valence formula and its applications	Carl, Ningije
3rd April 2019	The classical Theta function and the Riemann \(\zeta\)-function	Jakob, Kevin
10th April 2019	The Petersson inner product and Poincaré series	Kai, Lang
17th April 2019	Hecke operators and \(L\)-functions of modular forms	Muze, Amr
8th May 2019	No class
15th May 2019	The Weight \(2\) Eisenstein series and Jacobi's Formulas for Sums of Squares	Francesco, Gilles
24th May 2019	The non-holomorphic Eisenstein Series	Thomas, Valentine
1st June 2019	The Class Number Formula	Robert, Paul

There will be no talks on the 24th April 2019 (easter break) and on the 1st May 2019.

Literature

• A Course in Arithmetic by J.-P. Serre (Springer 1973) 
• Modular Forms by T. Miyake (Springer 1989) 
• Introduction to Elliptic Curves and Modular Forms by N. Koblitz (Springer 1993) 
• A First Course in Modular Forms by F. Diamond and J. Shurman (Springer 2005) 
• Introduction to Modular Forms by S. Lang (Springer 1987) 
• The 1-2-3 of Modular Forms by J. Bruinier, G. van der Geer, G. Harder, and D. Zagier (Springer 2008)