The structure of the algebra generated by special values of multiple modular L-functions

• Project/Area Number: 26400013
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka University
• Principal Investigator: Ihara Kentaro 大阪大学, インターナショナルカレッジ, 准教授 (00467523)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: multiple L-function / multiple zeta values / elliptic modular form / multiple L function

Outline of Final Research Achievements

"The multiple modular L-functions" are introduced as a generalization of modular L-functions. Several special values of the functions are computed numerically. The algebraic structure of those values fully depends on the weights and levels of modular functions. An upper bound of the size of the algebra is given explicitly in this research.

Research Products

• [Int'l Joint Research] Korea Institute for Advanced Study(韓国)
• [Int'l Joint Research] U.S. Naval Academy(米国)
• [Journal Article] Quasi-shuffle products revisited (2017)
  • Author(s): Michael E. Hoffman, Kentaro Ihara
  • Journal Title: Journal of Algebra Volume: 481 Pages: 293-326
  • DOI: 10.1016/j.jalgebra.2017.03.005
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] Basic on modular L-functions (2016)
  • Author(s): Kentaro Ihara
  • Organizer: 大阪大学数学教室, 特別セミナー
  • Place of Presentation: 大阪大学 (大阪府豊中市)
• [Presentation] 保形L関数の多重化とその特殊値 (2015)
  • Author(s): Kentaro Ihara
  • Organizer: 東北大学整数論セミナー
  • Place of Presentation: 東北大学(宮城県、仙台市)
  • Year and Date: 2015-06-29
• [Presentation] On multiple modular L-values (2014)
  • Author(s): Kentaro Ihara
  • Organizer: Workshop on Multiple Zeta Value
  • Place of Presentation: 九州大学
  • Year and Date: 2014-08-22 – 2014-08-23