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

• 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
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• 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 / 類数

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).

Research Products

• [Journal Article] Edge colored complete graphs and a generalization of self complementarity (2015)
  • Author(s): Kumi Kobata and Yasuo Ohno
  • Journal Title: Utilitas Mathematica Volume: 印刷中
  • Peer Reviewed
• [Journal Article] GCD and LCM-like identities for ideals in commutative rings (2015)
  • Author(s): Daniel D. Anderson, Shuzo Izumi, Yasuo Ohno and Manabu Ozaki
  • Journal Title: Journal of Algebra and Its Applications Volume: 印刷中 Issue: 01 Pages: 1-12
  • DOI: 10.1142/s0219498816500109
  • Peer Reviewed / Open Access
• [Journal Article] Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms II (2014)
  • Author(s): Yasuo Ohno and Takashi Taniguchi
  • Journal Title: Mathematical Research Letters Volume: 21 Issue: 2 Pages: 363-378
  • DOI: 10.4310/mrl.2014.v21.n2.a12
  • Peer Reviewed / Open Access
• [Journal Article] Relations among Dirichlet series whose coefficients are classs numbers of binary cubic forms II (2014)
  • Author(s): Yasuo Ohno and Takashi Taniguchi
  • Journal Title: Mathematical Research Letters Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Periodicity on poly-Euler numbers and Vandiver type congruence for Euler numbers (2013)
  • Author(s): Yasuo Ohno and Yoshitaka Sasaki
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B44 Pages: 205-211
  • Peer Reviewed
• [Journal Article] On certain properties of poly-Bernoulli numbers with negative index (2013)
  • Author(s): Mika Sakata and Yasuo Ohno
  • Journal Title: Journal of the faculty of science and engineering Kinki University Volume: 49 Pages: 5-7
  • Peer Reviewed
• [Journal Article] Weighted lonesum matrices and related generating function (2013)
  • Author(s): Ken Kamano, Yasuo Ohno and Shuji Yamamoto
  • Journal Title: Integers Volume: 未定
  • Peer Reviewed
• [Journal Article] On the parity of poly-Euler numbers (2012)
  • Author(s): Yasuo Ohno and Yoshitaka Sasaki
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B32 Pages: 271-278
  • Peer Reviewed
• [Journal Article] On 3-variable exponential polynomials and quantum algorithms (2012)
  • Author(s): Yasuo Ohno, Yoshitaka Sasaki and Chika Yamazaki
  • Journal Title: Kinki University Series on Quantum Computing Volume: 4 Pages: 211-223
  • Peer Reviewed
• [Journal Article] Cyclic q-MZSV sum (2012)
  • Author(s): Yasuo Ohno, Jun-ichi Okuda and Wadim Zudilin
  • Journal Title: Journal of Number Theory Volume: 132 Pages: 144-155
  • Peer Reviewed
• [Journal Article] On a generating function for duality property of multiple zeta-star values (2011)
  • Author(s): Chika Yamazaki and Yasuo Ohno
  • Journal Title: Journal of the faculty of science and engineering Kinki University Volume: 47 Pages: 1-4
  • NAID: 120005736254
  • Peer Reviewed
• [Presentation] 等号付き多重ゼータ値の系譜 (2014)
  • Author(s): 大野泰生
  • Organizer: 第23回 関西多重ゼータ研究会
  • Place of Presentation: 大阪工業大学
  • Year and Date: 2014-12-06
• [Presentation] 多重ゼータ値の関係式と母関数 (2014)
  • Author(s): 大野泰生
  • Organizer: 岡山大学理学部数学教室 代数学セミナー
  • Place of Presentation: 岡山大学
  • Year and Date: 2014-11-13
  • Invited
• [Presentation] 多重ゼータ値の線形関係式について (2014)
  • Author(s): 大野泰生
  • Organizer: 小山高専 数学談話会
  • Place of Presentation: 小山工業高等専門学校
  • Year and Date: 2014-10-28
  • Invited
• [Presentation] Eulerの多重ゼータ値と母関数 (2014)
  • Author(s): 大野泰生
  • Organizer: 立教大学 数理物理学セミナー
  • Place of Presentation: 立教大学
  • Year and Date: 2014-10-01
  • Invited
• [Presentation] Sums of multiple zeta values and their generating functions (2014)
  • Author(s): Yasuo Ohno
  • Organizer: The 2nd Japan-Taiwan Joint Conference on Number Theory
  • Place of Presentation: 国民休暇村気仙沼大島・宮城県
  • Year and Date: 2014-09-01
• [Presentation] Multiple zeta values and hypergeometric functions (2014)
  • Author(s): Yasuo Ohno
  • Organizer: Workshop on Multiple Zeta Values
  • Place of Presentation: 九州大学
  • Year and Date: 2014-08-22
  • Invited
• [Presentation] 多重ゼータ値と母関数 (2014)
  • Author(s): 大野泰生
  • Organizer: 裏磐梯数学セミナー
  • Place of Presentation: 裏磐梯高原ホテル・福島県北塩原村
  • Year and Date: 2014-07-30 – 2014-07-31
  • Invited
• [Presentation] 等号付き多重ゼータ値について (2014)
  • Author(s): 大野泰生
  • Organizer: 東北大学理学研究科数学専攻 整数論セミナー
  • Place of Presentation: 東北大学理学研究科
  • Year and Date: 2014-06-09
• [Presentation] 多重ゼータ値と多重ベルヌーイ数 (2014)
  • Author(s): 大野泰生
  • Organizer: One-day workshop around Algebraic Combinatorics
  • Place of Presentation: 高知大学
  • Year and Date: 2014-06-07
  • Invited
• [Presentation] 多重ゼータ値の和公式と双対公式について (2014)
  • Author(s): 大野泰生
  • Organizer: 東北大学理学研究科数学教室 談話会
  • Place of Presentation: 東北大学理学研究科
  • Year and Date: 2014-04-21
• [Presentation] 大野泰生 (2012)
  • Author(s): On the enumeration of certain edge-colored graphs
  • Organizer: RIMS研究集会・有限群とその表現、頂点作用素代数、組合せ論の研究(招待講演)
  • Place of Presentation: 京都大学数理解析研究所（京都市）
• [Presentation] 辺着色hypergraphにおける巡回自己同型について (2011)
  • Author(s): 小畑久美・大野泰生
  • Organizer: 日本数学会・秋季総合分科会・応用数学分科会
  • Place of Presentation: 信州大学（松本市）
• [Presentation] 重みつきロンサム行列について (2011)
  • Author(s): 大野泰生・鎌野健・山本修司
  • Organizer: 日本数学会・秋季総合分科会・代数学分科会
  • Place of Presentation: 信州大学（松本市）
• [Presentation] 多重Euler数の数論的性質 (2011)
  • Author(s): 大野泰生・佐々木義卓
  • Organizer: 日本数学会・秋季総合分科会・代数学分科会
  • Place of Presentation: 信州大学（松本市）
• [Presentation] Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms II (2011)
  • Author(s): 大野泰生・谷口隆
  • Organizer: 日本数学会・秋季総合分科会・代数学分科会
  • Place of Presentation: 信州大学（松本市）
• [Presentation] A view of Hoffman's basis and two-one formula for multiple zeta values (2011)
  • Author(s): 大野泰生
  • Organizer: RIMS研究集会・解析数論シンポジウム(招待講演)
  • Place of Presentation: 京都大学数理解析研究所（京都市）
• [Presentation] 2元3次形式の簡約理論と類対応の観察 (2011)
  • Author(s): 大野泰生
  • Organizer: 北陸数論研究集会(招待講演)
  • Place of Presentation: 金沢大学サテライトプラザ（金沢市）
• [Presentation] On multiple zeta-star values
  • Author(s): Yasuo Ohno
  • Organizer: Workshop on Grothendieck-Teichmueller Theory and Multiple Zeta Values
  • Place of Presentation: Isaac Newton Institute for Mathematical Sciences・Cambridge大学・イギリス
  • Invited
• [Presentation] 多重ゼータ値の関係式入門
  • Author(s): 大野泰生
  • Organizer: RIMS研究集会「多重ゼータ値の諸相」
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] 多重Euler数の諸性質について
  • Author(s): 佐々木義卓・大野泰生
  • Organizer: 第10回「代数学と計算」研究集会（AC2013）
  • Place of Presentation: 首都大学東京
• [Presentation] On Relations among Multiple Zeta Values
  • Author(s): Yasuo Ohno
  • Organizer: 2012 NCTS Japan-Taiwan Joint Conference on Number Theory
  • Place of Presentation: National Center for Theoretical Science・新竹・台湾
  • Invited
• [Presentation] On a property of di-Bernoulli numbers
  • Author(s): Yasuo Ohno
  • Organizer: 第１７回早稲田大学整数論研究集会2012
  • Place of Presentation: 早稲田大学
  • Invited
• [Presentation] 2重ベルヌーイ数の2-orderと3-orderについて
  • Author(s): 坂田実加・大野泰生
  • Organizer: 日本数学会・年会・代数学分科会
  • Place of Presentation: 京都大学