2022 Fiscal Year Final Research Report
Generalizations of the double shuffle relations for multiple zeta values and the connections to modular forms
Project/Area Number |
21K13771
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Research Category |
Grant-in-Aid for Early-Career Scientists
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Allocation Type | Multi-year Fund |
Review Section |
Basic Section 11010:Algebra-related
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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)
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Project Period (FY) |
2021-04-01 – 2023-03-31
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Keywords | Multiple zeta values / Modular forms |
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.
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Free Research Field |
Number theory
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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.
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