MODULAR FORMS
| Title | MODULAR FORMS / MODULAR FORMS |
| Code | Θ014 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Angelos Koutsianas |
| Common | Yes |
| Status | Active |
| Course ID | 600025894 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Spring | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Spring |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268418
|
Course Type 2021
Specific Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268418
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
Prerequisites
Required Courses
- Θ020 COMPLEX ANALYSIS
General Prerequisites
Elementary Number Theory, Complex Analysis, Algebraic Number Theory
Learning Outcomes
- Introduction to the basic properties of modular forms
- Modular curves
- Hecke operators and q-expansions
- Newforms
General Competences
- Apply knowledge in practice
- Work autonomously
- Work in teams
- Advance free, creative and causative thinking
Course Content (Syllabus)
The group SL2(Z) and congruence subgroups. Definition of modular forms and q-expansion. Modular curves as Riemann surfaces, moduli space. Dimension formulas of spaces of modular forms. Petersson inner product. Eisenstein series. Hecke operators and newforms. Abelian varieties and modular curves. Eichler-Shimura relation and L-functions. Galois representations.
Keywords
modular forms
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ✓ | ✓ | ||
| Reading Assigment | 258 | ✓ | ✓ | ||
| Exams | 3 | ✓ | ✓ | ||
| Total | 300 |
Student Assessment
Description
Assignments: There are 2 series of exercises during the semester. The first in the middle of the semester and the second at the end. The assignments are mandatory and contribute to the 40% of the final grade.
Grade: There is only oral or written exam. The final grade is computed by
- 60% of the oral or written exam
- 40% of the assignments
Student Assessment methods
- Written Exam with Multiple Choice Questions (Formative, Summative)
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
- Performance / Staging (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
1 - Diamond F., Shurman J., A First Course in Modualr Forms.
2 - Lang S., Introduction to Modular Forms.
3 - Koblitz N., Introduction to Elliptic Curves and Modular Forms.
4 - Apostol T., Modular Functions and Dirichlet Series in Number Theory.
5 - Serre J.-P., A Course in Arithmetic. "
Last Update
29-11-2024
