This module is part of a long-term overall curriculum plan for the Master's programme, which ensures that modules with an amount of at least 20 CP are offered in all five fields each year. The module is offered at irregular intervals as part of this overall curriculum planning.
10 Credit points
For information on the duration of the modul, refer to the courses of study in which the module is used.
Non-official translation of the module descriptions. Only the German version is legally binding.
Students master the basic contents and methods of the theory of modular forms, in particular they can independently carry out very complex proofs in this area requiring a high level of mathematical expertise. Students are able to define central concepts of the theory (e.g. modular forms, Hecke operators, L-functions) and apply them in context. They are able to combine methods from different areas, namely complex analysis, algebra and number theory.
Accordingly, students recognise further-reaching connections to mathematical facts already acquired. They can transfer and apply the knowledge and methods they have learnt so far to deeper mathematical problems. Students also expand their mathematical intuition as a result of more intensive study.
In the tutorials, students develop their ability to discuss mathematical topics and thus further prepare themselves for the requirements of the Master's module, in particular for the scientific discussion within the Master's seminar presentation and the defence of their Master's thesis.
The following basic content of teaching from the field of Modular Forms is compulsory:
Modular group and upper half-plane, Modular forms for the modular group, Hecke theory, L-functions, Modular forms for congruence subgroups, Modular curves as Riemann surfaces
In addition, the following content of teaching can be covered, for example:
Modular forms of half-integral weight, singular moduli, real-analytic modular forms, Modular curves as algebraic curves and as moduli spaces, Eichler-Shimura theory
Basic knowledge in complex analysis, algebra and some basic number theory
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Module structure: 1 SL, 1 bPr 1
| Allocated examiner | Workload | LP2 |
|---|---|---|
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Teaching staff of the course
Tutorials Introduction to Modular Forms
(exercise)
Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises. |
see above |
see above
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(electronic) written examination in presence of usually 120 minutes, oral examination in presence or remote of usually 40 minutes, A remote electronic written examination is not permitted.
| Degree programme | Profile | Recommended start 3 | Duration | Mandatory option 4 |
|---|---|---|---|---|
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Mathematics | 2. o. 3. | one semester | Compulsory optional subject |
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Economics | 2. o. 3. | one semester | Compulsory optional subject |
| Mathematics / Master of Science [FsB vom 28.02.2025] | 2. o. 3. | one semester | Compulsory optional subject |
The system can perform an automatic check for completeness for this module.