课程信息
4.7
11 个评分
3 个审阅
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
高级

高级

完成时间(小时)

完成时间大约为54 小时

建议:12 weeks of study, 3-5 hours per week...
可选语言

英语(English)

字幕:英语(English)
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
高级

高级

完成时间(小时)

完成时间大约为54 小时

建议:12 weeks of study, 3-5 hours per week...
可选语言

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 1 小时

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 个视频 (总计 14 分钟), 5 个阅读材料
Video1 个视频
Reading5 个阅读材料
Pre-Course Survey10分钟
Course Overview10分钟
Grading and Logistics10分钟
Suggested Readings10分钟
About the Instructor10分钟
完成时间(小时)
完成时间为 3 小时

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 个视频 (总计 62 分钟), 1 个测验
Video5 个视频
Motivations12分钟
Theta-function12分钟
Modular and abelian transformations12分钟
Pullbacks of theta-function12分钟
Modular forms12分钟
2
完成时间(小时)
完成时间为 3 小时

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 个视频 (总计 75 分钟), 1 个测验
Video6 个视频
Definition of Jacobi forms (part 2)13分钟
Basic properties of Jacobi forms12分钟
Jacobi modular group11分钟
Symplectic group11分钟
Jacobi modular group (part 2)13分钟
3
完成时间(小时)
完成时间为 3 小时

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 个视频 (总计 86 分钟), 1 个测验
Video6 个视频
The action of Jacobi modular group14分钟
The action of Jacobi modular group (part 2)10分钟
The second definition of Jacobi forms15分钟
Special values of Jacobi forms11分钟
The first theorem20分钟
4
完成时间(小时)
完成时间为 3 小时

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 个视频 (总计 76 分钟), 1 个测验
Video6 个视频
The zeros of Jacobi forms (part 2)11分钟
Taylor expansion of Jacobi forms12分钟
Taylor expansion of Jacobi forms (part 2)13分钟
Dimensions of some spaces of Jacobi forms10分钟
Examples of Jacobi modular forms14分钟

讲师

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Valery Gritsenko

Laboratory of Algebraic Geometry and its Applications

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