Studies on quantum integrable systems and multiple zeta functions

• Project/Area Number: 25400026
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Rikkyo University
• Principal Investigator: KOMORI Yasushi 立教大学, 理学部, 准教授 (80343200)
• Co-Investigator(Renkei-kenkyūsha): MATSUMOTO Kohji 名古屋大学, 多元数理科学研究科, 教授 (60192754) ; TSUMURA Hirofumi 首都大学東京, 理工学研究科, 教授 (20310419)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 量子可積分系 / 多重ゼータ関数 / ルート系 / 楕円超幾何関数

Outline of Final Research Achievements

Both partition functions in quantum gauge theories and zeta-functions in mathematics, which play fundamental and important roles in each area, happen to coincide in some cases. Among them are the Witten zeta-functions. These zeta-functions are the main objects and should be studied from various viewpoints. For this problem, we proposed lattice sums associated with hyperplane arrangements and established a unified way to treat these values and functional relations among Witten zeta-functions via their generating functions. We also studied some properties of related zeta-functions and hypergeometric functions, and obtained new functional relations and formulas.

Research Products

• [Journal Article] Desingularization of complex multiple zeta-functions (2017)
  • Author(s): Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
  • Journal Title: American Journal of Mathemtaics Volume: 139 Issue: 1 Pages: 147-173
  • DOI: 10.1353/ajm.2017.0002
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Fundamentals of p-adic multiple L-functions and evaluation of their special values (2017)
  • Author(s): Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
  • Journal Title: Selecta Mathematica Volume: 23 Issue: 1 Pages: 39-100
  • DOI: 10.1007/s00029-016-0233-2
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Duality transformation formulas for multiple elliptic hypergeometric series of type BC (2016)
  • Author(s): Y. Komori, Y. Masuda and M. Noumi
  • Journal Title: Constr. Approx. Volume: 印刷中 Issue: 3 Pages: 483-516
  • DOI: 10.1007/s00365-015-9316-0
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Zeta-functions of weight lattices of compact semisimple connected Lie groups (2015)
  • Author(s): Y. Komori, K. Matsumoto and H. Tsumura
  • Journal Title: Siauliai Math. Semin. Volume: 10 Pages: 149-179
  • Peer Reviewed
• [Journal Article] On the zeros of Weng zeta functions for Chevalley groups (2015)
  • Author(s): H. Ki, Y. Komori and M. Suzuki
  • Journal Title: Manuscripta Math. Volume: 印刷中 Issue: 1-2 Pages: 119-176
  • DOI: 10.1007/s00229-015-0736-8
  • Peer Reviewed
• [Journal Article] Infinite series involving hyperbolic functions (2015)
  • Author(s): Y. Komori, K. Matsumoto and H. Tsumura
  • Journal Title: Lith. Math. J Volume: 55 Issue: 1 Pages: 102-118
  • DOI: 10.1007/s10986-015-9268-x
  • Peer Reviewed
• [Journal Article] On Witten multiple zeta-functions associated with semisimple Lie algebras V (2015)
  • Author(s): Y. Komori, K. Matsumoto and H. Tsumura
  • Journal Title: Glasg. Math. J Volume: 57 Issue: 1 Pages: 107-130
  • DOI: 10.1017/s0017089514000160
  • Peer Reviewed
• [Journal Article] Lattice sums of hyperplane arrangements (2014)
  • Author(s): Y. Komori, K. Matsumoto and H. Tsumura
  • Journal Title: Comment. Math. Univ. St. Pauli Volume: 63 Pages: 161-213
  • Peer Reviewed
• [Journal Article] Spherical functions on the space of p-adic unitary hermitian matrices II, the case of odd size (2014)
  • Author(s): Y. Hironaka and Y. Komori
  • Journal Title: Comment. Math. Univ. St. Pauli Volume: 63 Pages: 47-78
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Spherical functions on the space of $p$-adic unitary hermitian matrices (2014)
  • Author(s): Yumiko Hironaka, Yasushi Komori
  • Journal Title: International Journal of Number Theory Volume: 10 Issue: 02 Pages: 513-558
  • DOI: 10.1142/s1793042113501066
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] 荒川-金子ゼータ関数の GL_2(C) 拡張とその関数関係式について (2016)
  • Author(s): 小森 靖
  • Organizer: 関西多重ゼータ研究会
  • Place of Presentation: 大阪大学（大阪府豊中市）
  • Year and Date: 2016-12-03
  • Invited
• [Presentation] Zeta-functions of root systems and Poincare polynomials of Weyl groups (2016)
  • Author(s): Y. Komori
  • Organizer: Problems and Prospects in Analytic Number Theory
  • Place of Presentation: 京都大学（京都府京都市）
  • Year and Date: 2016-10-31
• [Presentation] On Arakawa-Kaneko zeta-functions associated with GL_2(C) and their functional relations (2016)
  • Author(s): 小森 靖
  • Organizer: 解析数論セミナー
  • Place of Presentation: 名古屋大学（愛知県名古屋市）
  • Year and Date: 2016-06-17
• [Presentation] 超平面配置の格子和とその応用 (2015)
  • Author(s): 小森 靖
  • Organizer: 関西多重ゼータ研究会
  • Place of Presentation: 立命館大学びわこ・くさつキャンパス(滋賀県草津市)
  • Year and Date: 2015-10-17
• [Presentation] Lattice sums of hyperplane arrangements and their applications (2015)
  • Author(s): Y. Komori
  • Organizer: French-Japanese Workshop on multiple zeta functions and applications
  • Place of Presentation: St-Etienne, France
  • Year and Date: 2015-09-07
  • Int'l Joint Research
• [Presentation] Desingularization of complex multiple zeta-functions and fundamentals of p-adic multiple L-functions I (2013)
  • Author(s): Y. Komori
  • Organizer: RIMS 研究集会
  • Place of Presentation: 京都大学