A study on algebraic and analytic behavior of multiple zeta-functions and multiple automorphic L-functions

2017 Fiscal Year Final Research Report

• Project/Area Number: 25287002
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Nagoya University
• Principal Investigator: Matsumoto Kohji 名古屋大学, 多元数理科学研究科, 教授 (60192754)
• Co-Investigator(Kenkyū-buntansha): 小森 靖 立教大学, 理学部, 教授 (80343200)
• Co-Investigator(Renkei-kenkyūsha): TSUMURA HIROFUMI 首都大学東京, 大学院理工学研究科, 教授 (20310419) ; KANEKO MASANOBU 九州大学, 大学院数理学研究院, 教授 (70202017) ; OHNO YASUO 東北大学, 大学院理学研究科, 教授 (70330230) ; SHOJI MAYUMI 日本女子大学, 理学部, 教授 (10216161) ; FURUSHO HIDEKAZU 名古屋大学, 大学院多元数理科学研究科, 准教授 (60377976) ; YAMASAKI YOSHINORI 愛媛大学, 大学院理工学研究科, 准教授 (00533035) ; UMEGAKI YUMIKO 奈良女子大学, 理学部, 准教授 (80372689) ; NAKAMURA TAKASHI 東京理科大学, 理工学部, 講師 (50532355)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 多重ゼータ関数 / ルート系のゼータ関数 / 関数等式 / 関数関係式 / p進多重ゼータ関数 / 多重保型 L 関数 / 特異点解消多重ゼータ関数

Outline of Final Research Achievements

The present research has dealt with various multiple series, such as multiple zeta-functions of Euler-Zagier type, a more general class of zeta-functions of root systems, and also the same type of series with Fourier coefficients of modular forms on the numerators. The main results obtained in the period of the present research are the structure theory and functional relations for zeta-functions of root systems, or more general multiple zeta-functions associated with Lie groups; evaluation of values of multiple series involving hyperbolic functions; numerical computations on the zeros multiple zeta-functions; the proof of two types of functional equations for double zeta-functions involving Fourier coefficients of modular forms on the numerator; the idea of desingularized multiple zeta-functions and the development of the theory of p-adic multiple zeta-functions.

Free Research Field

整数論