About this Course

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Advanced Level
Approx. 30 hours to complete
English
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Advanced Level
Approx. 30 hours to complete
English

Offered by

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National Research University Higher School of Economics

Syllabus - What you will learn from this course

Week
1

Week 1

1 hour to complete

Introduction to the Course

1 hour to complete
2 videos (Total 16 min), 5 readings
2 videos
About the Course14m
5 readings
About the University10m
Course Overview10m
Grading and Logistics10m
Suggested Readings10m
About the Instructor10m
2 hours to complete

Jacobi modular forms: motivations

2 hours to complete
5 videos (Total 62 min)
5 videos
Theta-function12m
Modular and abelian transformations12m
Pullbacks of theta-function12m
Modular forms12m
Week
2

Week 2

2 hours to complete

Jacobi modular forms: the first definition

2 hours to complete
6 videos (Total 75 min)
6 videos
Definition of Jacobi forms (part 2)13m
Basic properties of Jacobi forms12m
Jacobi modular group11m
Symplectic group11m
Jacobi modular group (part 2)13m
Week
3

Week 3

2 hours to complete

Jacobi modular group and the second definition of Jacobi forms. Special values of Jacobi modular forms

2 hours to complete
6 videos (Total 86 min)
6 videos
The action of Jacobi modular group14m
The action of Jacobi modular group (part 2)10m
The second definition of Jacobi forms15m
Special values of Jacobi forms11m
The first theorem20m
Week
4

Week 4

2 hours to complete

Zeros of Jacobi forms. The Jacobi theta-series, the Dedekind eta-function and the first examples of Jacobi modular forms

2 hours to complete
6 videos (Total 76 min)
6 videos
The zeros of Jacobi forms (part 2)11m
Taylor expansion of Jacobi forms12m
Taylor expansion of Jacobi forms (part 2)13m
Dimensions of some spaces of Jacobi forms10m
Examples of Jacobi modular forms14m

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