Markus Schwagenscheidt: Katalogdaten im Frühjahrssemester 2021 |
| Name | Herr Dr. Markus Schwagenscheidt |
| Adresse | Imamoglu, Oezlem (Tit.-Prof.) ETH Zürich, HG J 14.3 Rämistrasse 101 8092 Zürich SWITZERLAND |
| markus.schwagenscheidt@math.ethz.ch | |
| URL | http://www.markus-schwagenscheidt.de |
| Departement | Mathematik |
| Beziehung | Dozent |
| Nummer | Titel | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|
| 401-3110-21L | Student Seminar in Number Theory: Modular Forms  Number of participants limited to 26. | 4 KP | 2S | M. Schwagenscheidt | |
| Kurzbeschreibung | Seminar on the basic theory of classical elliptic modular forms | ||||
| Lernziel | In the seminar we will learn about the basic theory of classical elliptic modular forms. We start with the action of the modular group on the complex upper half-plane by Moebius transformations and describe its fundamental domain. As first examples of modular forms, we will investigate Eisenstein series, Ramanujan's Delta function, the Dedekind eta function, and the modular j-invariant. We will show that the space of modular forms of a fixed weight is finite dimensional, and determine its dimension. We will also study Hecke operators and the Petersson inner product on spaces of modular forms, and the L-functions associated with modular forms. Towards the end of the seminar we will discuss some more advanced topics, such as differential operators and quasimodular forms, the CM values of the j-function, and the periods of modular forms. | ||||
| Skript | https://people.math.ethz.ch/~mschwagen/modulformenSS19/modulformen2019_skript.pdf | ||||
| Literatur | Cohen, Strömberg: Modular Forms: A Classical Approach Diamond, Shurman: A first course in modular forms Koblitz: Introduction to elliptic curves and modular forms Koecher, Krieg: Elliptische Funktionen und Modulformen Lang: Introduction to modular forms Miyake: Modular forms Serre: A course in arithmetic Zagier: The 1-2-3 of modular forms Lecture notes on modular forms, available online: https://people.math.ethz.ch/~mschwagen/modulformenSS19/modulformen2019_skript.pdf | ||||
| Voraussetzungen / Besonderes | We will need the fundamental results from complex analysis, and some elementary group theory. The website of the seminar can be found at https://people.math.ethz.ch/~mschwagen/modularforms | ||||