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2019 Fiscal Year Final Research Report

The outlook for the dimension conjecture and the study of Lie algebras of multiple zeta values and multiple Eisenstein series

Research Project

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Project/Area Number 18K13393
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 11010:Algebra-related
Research InstitutionAichi Prefectural University

Principal Investigator

Tasaka Koji  愛知県立大学, 情報科学部, 講師 (30780762)

Project Period (FY) 2018-04-01 – 2020-03-31
Keywords多重ゼータ値 / モジュラー形式
Outline of Final Research Achievements

We study a conjecture proposed by Broadhurst and Kreimer in 1997 stating mysterious relationships between multiple zeta values (real numbers) and modular forms (holomorphic function on the complex upper-half plane). One of the upshots of this project is a newly analytic interpretation of the so-called "modular relation (an explicit correspondence between double zeta values and modular forms)", which was first established by Gangl, Kaneko and Zagier in 2006.

Free Research Field

整数論

Academic Significance and Societal Importance of the Research Achievements

近年,モジュラー関係式を一つの動機として,多重ゼータ値とモジュラー形式を共通の枠組みで捉える研究がヨーロッパを中心にいくつかおこっている。世界的な視点では,むしろ幾何的な方面からのアプローチが盛んであるが,本研究では内在する組合せ的な構造やモジュラー形式の解析理論などに新しい貢献ができたという点において,有意義である。

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Published: 2021-02-19  

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