240904 Modulformen (V) (SoSe 2012)
Contents, comment
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"Es gibt fünf Grundrechenarten: Addition, Subtraktion, Multikplikation, Division und Modulformen." (Martin Eichler)
Modulformen sind holomorphe Funktionen auf der oberen Halbebene, die ein einfaches Transformationsverhalten unter gebrochen rationalen Transformationen aufweisen.
Einerseits haben Modulformen vielfältige Anwendungen in der Zahlentheorie (sie spielen zB eine zentrale Rolle beim Beweis der Fermat-Vermutung), andererseits kann man explizite Rechnungen mit ihnen durchführen (diverse Computeralgebraprogramme wie zB SAGE haben Pakete zum Rechnen mit Modulformen).mögliche Themen:
-L-Reihen und Hecke-Operatoren
-Gitter und Thetareihen
-Eisensteinreihen und die Rankin-Selberg-Methode
-Modulare Symbole, Computeralgebra und p-adische L-Funktionen
-Modulräume und elliptische Kurven
Requirements for participation, required level
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Vorkenntnisse: LA I+II und Analysis I+II, Funktionentheorie
(Die benötigten Resultate aus der Funktionentheorie können bei Bedarf in den Übungen behandelt werden.)
Bibliography
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Bücher:
J.H. Bruinier, G. Harder, G. van der Geer, D. Zagier: The 1-2-3 of modular forms
D. Bump: Automorphic forms and representations
A. Deitmar: Automorphe Formen
F. Diamond, J. Shurman: A first course in modular forms
H. Hida: Elementary theory of L-functions and Eisenstein series
T. Miyake: Modular forms
J.-P. Serre: A Course in Arithmetic
G. Shimura: Introduction to the arithmetic theory of automorphic formsOnline Skripte:
J. Milne: Modular Functions and Modular Forms
K. Ribet, W. Stein: Lectures on Modular Forms and Hecke Operators
W. Stein: Modular Forms: A Computational Approach
G. Wiese: Vorlesung über Modulformen
Teaching staff
Dates ( Calendar view )
| Frequency | Weekday | Time | Format / Place | Period | |
|---|---|---|---|---|---|
| weekly | Mo | 16-18 | V2-200 | 02.04.-13.07.2012
not on: 4/9/12 / 5/28/12 |
|
| weekly | Do | 16-18 | V2-200 | 02.04.-13.07.2012
not on: 5/17/12 / 6/7/12 |
Subject assignments
| Degree programme/academic programme | Validity | Variant | Subdivision | Status | Semester | LP | |
|---|---|---|---|---|---|---|---|
| Mathematik / Bachelor | (Enrollment until SoSe 2011) | Kern- und Nebenfach | MM09a | Pflicht | |||
| Mathematik / Diplom | (Enrollment until SoSe 2008) | Pflicht | 4. 5. 6. 7. 8. | GS und HS | |||
| Mathematik / Master | (Enrollment until SoSe 2011) | MM01S; MM05S; MM06S |
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- Monday, February 13, 2012
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- Monday, February 13, 2012
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- lecture (V) / 4
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- Faculty of Mathematics
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