Research on multiple zeta value and calculation technology by a formula of systems of Boolean polynomial equations

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K03727
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12030:Basic mathematics-related
• Research Institution: International Professional University of Technology in Tokyo (2023); National Institute of Informatics (2020-2022)
• Principal Investigator: Tomoya Machide 東京国際工科専門職大学, 情報工学科, 講師 (60614526)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 多重ゼータ値 / Boolean多項式 / ガウスの消去法 / 充足可能性問題(SAT) / 彩色問題 / Alon-Tarsi多項式

Outline of Final Research Achievements

In this research, we try to collaborate with subjects of mathematics and Computer science: the subject of mathematics is the multiple zeta value (MZV) in number theory, and that of Computer science is the Boolean satisfiability problem (SAT) in propositional logic. As an application from the latter to the former, we were able to calculate ranks of linear relations of MZVs. As an application from the former to the latter, we developed the algorithm via the formula for systems of Boolean polynomial equations. We also use the knowledge of natural language processing (NLP).

Free Research Field

解析的整数論、SAT、自然言語処理

Academic Significance and Societal Importance of the Research Achievements

本研究では数学の多重ゼータ値と計算機科学のSAT問題の結果を互いに応用した。また応用の際は自然言語処理の知識と経験を用いた。このことは研究の他分野連携を促進する。異なる分野の連携は思いもかけない発展につながる可能性が高く、昨今の大規模言語モデルの隆盛とともに、今後さらなる融合が考えられる。実際、多重ゼータ値の線形関係式の整数係数を mod 2 の条件下（つまり真偽の２値の条件下）で考察した場合、不可思議な法則があることが発見された。