Studies of zeta functions of prehomogeneous vector spaces and multiple zeta values

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540036
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Tohoku University (2014); Kinki University (2011-2013)
• Principal Investigator: OHNO YASUO 東北大学, 理学(系)研究科(研究院), 教授 (70330230)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 多重ゼータ値 / 多重ベルヌーイ数 / 2元3次形式 / 概均質ベクトル空間 / 多重ゼータ関数 / 多重オイラー数 / ロンサム行列 / 簡約理論

Outline of Final Research Achievements

We mainly studied multiple zeta and zeta-star values, poly-Bernoulli and poly-Euler numbers, and class numbers of binary cubic forms. In particular, we gave representations using special values of hypergeometric functions for generating functions of certain series of multiple zeta and zeta-star values. We also studied basic or p-adic properties of poly-Bernoulli and poly-Euler numbers and class numbers of integral binary cubic forms under the action of congruence subgroups of SL(2,Z).

Free Research Field

数論