課程信息
4.7
11 個評分
3 個審閱
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
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可靈活調整截止日期

根據您的日程表重置截止日期。
高級

高級

完成時間(小時)

完成時間大約為54 小時

建議:12 weeks of study, 3-5 hours per week...
可選語言

英語(English)

字幕:英語(English)...
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
高級

高級

完成時間(小時)

完成時間大約為54 小時

建議:12 weeks of study, 3-5 hours per week...
可選語言

英語(English)

字幕:英語(English)...

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 1 小時

Introduction to the Course

Welcome to the course! I hope you have an opportunity to reserve some time to explore the course content, course logic and our grading policy. The course consists of 12 lectures. This course will help you to start your progress in the field of the theory of Jacobi modular forms. Best regards, Valery Gritsenko...
Reading
1 個視頻(共 14 分鐘), 5 個閱讀材料
Video1 個視頻
Reading5 個閱讀材料
Pre-Course Survey10分鐘
Course Overview10分鐘
Grading and Logistics10分鐘
Suggested Readings10分鐘
About the Instructor10分鐘
完成時間(小時)
完成時間為 3 小時

Jacobi modular forms: motivations

This module is devoted to motivations to study Jacobi forms. We provide some first examples including theta-functions. Also there is a peer review in the end of this module....
Reading
5 個視頻(共 62 分鐘), 1 個測驗
Video5 個視頻
Motivations12分鐘
Theta-function12分鐘
Modular and abelian transformations12分鐘
Pullbacks of theta-function12分鐘
Modular forms12分鐘
2
完成時間(小時)
完成時間為 3 小時

Jacobi modular forms: the first definition

This module is devoted to the first definition of Jacobi forms. In this module we also define Jacobi modular group. Also there is a peer review in the end of this module....
Reading
6 個視頻(共 75 分鐘), 1 個測驗
Video6 個視頻
Definition of Jacobi forms (part 2)13分鐘
Basic properties of Jacobi forms12分鐘
Jacobi modular group11分鐘
Symplectic group11分鐘
Jacobi modular group (part 2)13分鐘
3
完成時間(小時)
完成時間為 3 小時

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

This module is devoted to the second definition of Jacobi forms. In this module we also consider special values of Jacobi forms. Also there is a peer review in the end of this module....
Reading
6 個視頻(共 86 分鐘), 1 個測驗
Video6 個視頻
The action of Jacobi modular group14分鐘
The action of Jacobi modular group (part 2)10分鐘
The second definition of Jacobi forms15分鐘
Special values of Jacobi forms11分鐘
The first theorem20分鐘
4
完成時間(小時)
完成時間為 3 小時

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

This module is devoted to zeros of Jacobi modular forms, their Taylor extensions and the first examples of Jacobi forms. Using classical Jacobi theta-series and Dedekind eta-function we construct a series of Jacobi forms. Also there is a peer review in the end of this module....
Reading
6 個視頻(共 76 分鐘), 1 個測驗
Video6 個視頻
The zeros of Jacobi forms (part 2)11分鐘
Taylor expansion of Jacobi forms12分鐘
Taylor expansion of Jacobi forms (part 2)13分鐘
Dimensions of some spaces of Jacobi forms10分鐘
Examples of Jacobi modular forms14分鐘

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Valery Gritsenko

Laboratory of Algebraic Geometry and its Applications

關於 National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru...

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