Goals of the Course(JPN)
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.
Objectives of the Course(JPN))
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.
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,
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:
|Basic knowledge in Linear Algebra, Calculus and Algebra is necessary.
|Multiple zeta values and modular forms (Spring 2020): https://www.henrikbachmann.com/mzv2020.html
Course Evaluation Method and Criteria
|The evaluation will be done by homework assignments.
|There is no textbook, but we will create lecture notes during the course.
|Several references (lecture notes, research papers) can be found on the course homepage.
Study Load(Self-directed Learning Outside Course Hours)
|The students are expected to recall the previous lectures before coming to class.
Notice for Students
|Please always check the course homepage for regular updates: https://www.henrikbachmann.com/qmzv_fmzv.html
Propriety of Other department student's attendance
Conditions of Other department student's attendance
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.
Additional measures for remote class (on-demand class)