授業の目的 【日本語】
Goals of the Course(JPN) | | | この講義は英語で行われます。 また、英語が苦手な学生のために、日本語を少し取り入れた講義ノートを作成していく予定です。 |
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授業の目的 【英語】
Goals of the Course | | | This course will given an introduction to q-analogues of multiple zeta values and finite multiple zeta values. Both of these can be seen as variants of classical multiple zeta values. The goal of this lecture is to introduce the students to recent research results in this area and to offer possible research directions for master or PhD projects. |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | |
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到達目標 【英語】
Objectives of the Course | | | In this course, we will introduce and use various different tools from algebra, calculus and combinatorics. It is mainly aimed in students having a broad interest in number theory. If time permits we will also do some computer guided experiments which might be helpful for students to use in their own projects. |
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授業の内容や構成
Course Content / Plan | | The course will cover at least the following topic. A detailed course plan will be available on the course homepage:
Introduction to multiple zeta values,
q-analogues of multiple zeta values (qMZV),
finite multiple zeta values (FMZV),
regularized and symmetric multiple zeta values, the Kaneko-Zagier conjecture,
quasi-shuffle products,
double shuffle relations for qMZV and FMZV,
finite harmonic q-series at roots of unity,
the "BTT-Philosophy": Connection of q-analogues and finite MZV.
And always up-to-date course plan will be available on the course homepage:
https://www.henrikbachmann.com/qmzv_fmzv.html |
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履修条件
Course Prerequisites | | | Basic knowledge in Linear Algebra, Calculus and Algebra is necessary. |
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関連する科目
Related Courses | | | Multiple zeta values and modular forms (Spring 2020): https://www.henrikbachmann.com/mzv2020.html |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | | The evaluation will be done by homework assignments. |
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教科書・テキスト
Textbook | | | There is no textbook, but we will create lecture notes during the course. |
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参考書
Reference Book | | | Several references (lecture notes, research papers) can be found on the course homepage. |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | | The students are expected to recall the previous lectures before coming to class. |
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注意事項
Notice for Students | | | Please always check the course homepage for regular updates: https://www.henrikbachmann.com/qmzv_fmzv.html |
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他学科聴講の可否
Propriety of Other department student's attendance | | |
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他学科聴講の条件
Conditions of Other department student's attendance | | |
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レベル
Level | | |
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キーワード
Keyword | | |
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履修の際のアドバイス
Advice | | |
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授業開講形態等
Lecture format, etc. | | | The current plan is to do this lecture face-to-face. Depending on the situation we will offer online sessions for students who can not be in Nagoya. |
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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
Additional measures for remote class (on-demand class) | | |
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