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高级

完成时间大约为54 小时

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

英语(English)

字幕:英语(English)

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

根据您的日程表重置截止日期。

高级

完成时间大约为54 小时

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

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...
1 个视频 (总计 14 分钟), 4 个阅读材料
1 个视频
4 个阅读材料
Course Overview10分钟
Grading and Logistics10分钟
Suggested Readings10分钟
About the Instructor10分钟
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....
5 个视频 (总计 62 分钟), 1 个测验
5 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....
6 个视频 (总计 75 分钟), 1 个测验
6 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....
6 个视频 (总计 86 分钟), 1 个测验
6 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....
6 个视频 (总计 76 分钟), 1 个测验
6 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
5
完成时间为 3 小时

The Jacobi theta-series as Jacobi modular form. The basic Jacobi modular forms

This module is devoted to detailed study of Jacobi theta-series. We will discuss abelian, modular and some other properties of this function. Also there is a peer review in the end of this module....
6 个视频 (总计 84 分钟), 1 个测验
6 个视频
Properties of Jacobi theta-function9分钟
Properties of Jacobi theta-function (part 2)13分钟
Properties of Jacobi theta-function (part 3)15分钟
Construction of Jacobi forms using theta-series15分钟
Construction of Jacobi forms using theta-series (part 2)13分钟
6
完成时间为 4 小时

Theta-blocks, theta-quarks and the first Jacobi cusp form of weight 2

This module is devoted to very important notion of theta-blocks and theta-quarks. In this module we also construct the first Jacobi form of weight 2. Also there is a peer review in the end of this module....
7 个视频 (总计 96 分钟), 1 个测验
7 个视频
Theta-blocks14分钟
Theta-blocks (part 2)13分钟
Theta-quarks14分钟
Dimension of the space of Jacobi forms of odd weight14分钟
Theta-quarks (part 2)11分钟
The proof of theorem about theta-quarks16分钟
The first Jacobi cusp form of weight 210分钟
7
完成时间为 4 小时

Jacobi forms in many variables and the Eichler-Zagier Jacobi forms

This module is devoted to Jacobi forms in many variables. In this module we also define classical Eichler-Zagier Jacobi forms in terms of Jacobi forms in many variables. Also there is a peer review in the end of this module....
6 个视频 (总计 93 分钟), 1 个测验
6 个视频
Jacobi theta-series and Jacobi forms in many variables (part 2)15分钟
Hyperbolic reformulation14分钟
Examples of Jacobi forms in many variables14分钟
Examples of Jacobi forms in many variables (part 2)16分钟
Examples of Jacobi forms in many variables (part 3)16分钟
8
完成时间为 3 小时

Jacobi forms in many variables and the splitting principle. Theta-quarks as a pull-back. Weak Jacobi forms in many variables

In this module we continue studying Jacobi forms in many variables. Among other things we discuss splitting principle and realize theta-quarks as a pull-back. Also there is a peer review in the end of this module....
6 个视频 (总计 90 分钟), 1 个测验
6 个视频
Theta-quarks as pull-backs of Jacobi forms (part 2)16分钟
Theta-quarks as pull-backs of Jacobi forms (part 3)13分钟
The splitting principle15分钟
The splitting principle (part 2)16分钟
Weak Jacobi forms in many variables13分钟
9
完成时间为 3 小时

The Weil representation and vector valued modular forms. Jacobi forms of singular weight

This module is devoted to very useful notion of the Weil representation and vector-valued modular forms. In this module we also define Jacobi forms of singular weight. Also there is a peer review in the end of this module....
6 个视频 (总计 85 分钟), 1 个测验
6 个视频
The Weil representation (part 2)15分钟
Jacobi forms of singular weight14分钟
Jacobi forms of singular weight (part 2)15分钟
Jacobi forms of critical weight15分钟
Jacobi forms of critical weight (part 2)12分钟
10
完成时间为 3 小时

Quasi-modular Eisenstein series. The automorphic correction of Jacobi forms and Taylor expansions

This module is devoted to Quasi-modular Eisenstein series. In this module we also define the automorpic correction of Jacobi forms and its Taylor expansion that gives us the way to construct the series of Jacobi forms. Also there is a peer review in the end of this module....
6 个视频 (总计 84 分钟), 1 个测验
6 个视频
Differential operator D15分钟
Quasi-modular Eisenstein series15分钟
Automorphic correction and Taylor expansions13分钟
Automorphic correction of Jacobi forms in many variables12分钟
Automorphic correction of Jacobi forms in many variables (part 2)12分钟
11
完成时间为 3 小时

Modular differential operators. The graded ring of the weak Jacobi modular forms

This module is devoted to Modular differential operators. In this module we also consider the Jacobi forms as the space with the structure of the bigraded ring. Also there is a peer review in the end of this module....
6 个视频 (总计 90 分钟), 1 个测验
6 个视频
Heat operator14分钟
Heat operator (part 2)15分钟
Applications of differential operators for Jacobi forms11分钟
The graded ring of the weak Jacobi modular forms17分钟
Jacobi type forms in many variables14分钟
12
完成时间为 3 小时

Jacobi type forms and the generalisation of the Cohen-Kuznetsov-Zagier operator

The last module is devoted to Jacobi type forms. In this module we also consider the generalisation of the Cohen-Kuznetsov-Zagier operator. Also there is a peer review in the end of this module....
4 个视频 (总计 52 分钟), 1 个测验
4 个视频
A new proof of Cohen-Kuznetsov-Zagier theorem13分钟
A new proof of Cohen-Kuznetsov-Zagier theorem (part 2)9分钟
Cohen-Kuznetsov-Zagier theorem in case of many variables14分钟

讲师

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Valery Gritsenko

Laboratory of Algebraic Geometry and its Applications

关于 国立高等经济大学

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