| Project/Area Number |
21K13771
|
|---|
| Research Category |
Grant-in-Aid for Early-Career Scientists
|
| Allocation Type | Multi-year Fund |
|---|
| Review Section |
Basic Section 11010:Algebra-related
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
Bachmann Henrik 名古屋大学, 多元数理科学研究科(国際), G30特任准教授 (20813372)
|
|---|
| Project Period (FY) |
2021-04-01 – 2023-03-31
|
| Project Status |
Completed (Fiscal Year 2022)
|
| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | Multiple zeta values / Modular forms / multiple zeta values / Eisenstein series / modular forms / q-analogues of MZV / Kronecker function / double shuffle relations |
|---|
| Outline of Research at the Start |
In the first part of the research the algebraic setup of above objects will be defined. The goal will be to give an explicit connection to previous works on modular forms and multiple zeta values. In the second part the connection to other areas related to multiple zeta values will be made explicit.
|
| Outline of Final Research Achievements |
In this research project a generalization of the classical double shuffle relations of multiple zeta values were introduced and studied. This
new set of equations are motivated by multiple Eisenstein series introduced by Gangl-Kaneko-Zagier. It is defined by using the notion of
bimoulds and they are given by those bimoulds which are symmetril and swap invariant.
|
| Academic Significance and Societal Importance of the Research Achievements |
This research project proposed a new family of relations which seem to describe exaclty the relations satisfied by multiple Eisenstein series. They can be seen as a "modular" analouge of the classical double shuffle relations for multiple zeta values.
|
