| 授業の目的 【日本語】 | | Multiple zeta values are real numbers appearing in various areas of mathematics and theoretical physics. Especially in Japan, the theory of multiple zeta values is a highly active research field. On the other hand, modular forms are holomorphic functions in the upper half-plan satisfying certain symmetries. These functions occur naturally in connection with problems arising in many areas of mathematics. The goal of this lecture is to give a introduction to the theory of multiple zeta values and their connections to modular forms.
All information on this course will be available on the regularly updated course homepage: https://www.henrikbachmann.com/mzv2020.html |
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| 授業の目的 【英語】 | | |
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| 到達目標 【日本語】 | | | The goal of this lecture is to give an introduction to the topic which is close to current research topics. |
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| 到達目標 【英語】 | | |
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| 授業の内容や構成 | | We will start by giving a standard introduction to the theory of multiple zeta values. After this, we will discuss their algebraic structure and especially discuss their linear relations.
In the second part of the course, we will discuss different connections to the theory modular forms. |
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| 履修条件 | | | Standard undergraduate courses such as linear algebra and calculus are expected. Having background in complex analysis is helpful at some points but not mandatory. |
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| 成績評価の方法と基準 | | | The grading will be based on homework assignments. |
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| 教科書・テキスト | | | We will not use a textbook but the course will be structured after several research papers. It is planned to provide lecture notes during the lecture and various references at the beginning of the course. |
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| 参考書 | | | There will be an regularly updated list of references on the course homepage. |
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| 課外学習等（授業時間外学習の指示） | | |
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| 注意事項 | | | All information on this course will be available on the course homepage: https://www.henrikbachmann.com/mzv2020.html |
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| 他学科聴講の可否 | | |
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| 他学科聴講の条件 | | |
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| レベル | | |
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| キーワード | | | Riemann zeta value, multiple zeta values, iterated integrals, double shuffle relations, quasi-shuffle algebras, modular forms, (multiple-)eisenstein series, period polynomials |
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| 履修の際のアドバイス | | |
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| 授業開講形態等 | | |
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| 遠隔授業（オンデマンド型）で行う場合の追加措置 | | |
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