• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Study of L-functions and regulators of motives via special functions

Research Project

Project/Area Number 18K03234
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 11010:Algebra-related
Research InstitutionChiba University

Principal Investigator

Otsubo Noriyuki  千葉大学, 大学院理学研究院, 教授 (60332566)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2022: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsL関数 / モチーフ / 超幾何関数 / 周期 / レギュレーター / 虚数乗法論 / 有限体 / 特殊関数
Outline of Final Research Achievements

We described the periods and regulators of hypergeometric fibrations in terms of hypergeometric functions (joint work with M. Asakura). As an application, we gave formulas expressing hypergeometric functions and their special values in terms of the logarithm of algebraic functions and algebraic numbers (joint work with M. Asakura and T. Terasoma). We formulated l-adic and p-adic analogues of the Gross-Deligne conjecture on the periods of motives with complex multiplication, and proved them for motives of abelian type (joint work with B. Kahn). We discovered a method to prove in a uniform manner the various transformation formulas for classical hypergeometric functions. We gave a definition of generalized hypergeometric functions (including those with many variables) over finite fields, and established various fundamental properties.

Academic Significance and Societal Importance of the Research Achievements

超幾何関数は数学のさまざまな分野や物理学で現れる非常に重要な対象である.超幾何関数は数論においても重要であり,数論的なL関数(リーマン・ゼータ関数の一般化)との関係からも注目されている.L関数の特殊値は現代の数論における最も重要な研究対象の一つであり,周期やレギュレーターという幾何学的な不変量との関係が予想されている.本研究では,モチーフの周期やレギュレーターと超幾何関数との関係について多角的に調べた.特に,周期,レギュレーター,超幾何関数たちの数論的(l進的,p進的, モチーフ的)な類似物にについて基礎的な研究を行った.古典的な超幾何関数論に新たな視点を与えるということも期待できる.

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (30 results)

All 2022 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (5 results) Journal Article (6 results) (of which Peer Reviewed: 6 results,  Open Access: 2 results) Presentation (12 results) (of which Int'l Joint Research: 5 results,  Invited: 10 results) Remarks (5 results) Funded Workshop (2 results)

  • [Int'l Joint Research] Inatitut de Mathematiques de Jussieu(フランス)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Institut de Mathematiques de Jussieu(フランス)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Institut de Mathematiques de Jussieu(フランス)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Institut de Mathematiques de Jussieu(フランス)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Institut de Mathematiques de Jussieu(フランス)

    • Related Report
      2018 Research-status Report
  • [Journal Article] Product formulas for hypergeometric functions over finite fields2022

    • Author(s)
      Noriyuki Otsubo, Takato Senoue
    • Journal Title

      Research in Number Theory

      Volume: 8(4) Issue: 4 Pages: 1-12

    • DOI

      10.1007/s40993-022-00348-3

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A new approach to hypergeometric transformation formulas2021

    • Author(s)
      Noriyuki Otsubo
    • Journal Title

      Ramanujan Journal

      Volume: 55 Issue: 2 Pages: 793-816

    • DOI

      10.1007/s11139-020-00286-7

    • Related Report
      2021 Research-status Report 2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] A functional logarithmic formula for the hypergeometric function ${}_3F_2$2019

    • Author(s)
      Masanori Asakura and Noriyuki Otsubo
    • Journal Title

      Nagoya Math. J.

      Volume: 236 Pages: 29-46

    • DOI

      10.1017/nmj.2018.33

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] An algebro-geometric study of special values of hypergeometric functions ${}_3F_2$2018

    • Author(s)
      Masanori Asakura, Noriyuki Otsubo and Tomohide Terasoma
    • Journal Title

      Nagoya Math. J.

      Volume: First View Pages: 1-16

    • DOI

      10.1017/nmj.2018.36

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] CM periods, CM regulators and hypergeometric functions, I2018

    • Author(s)
      Asakura Masanori、Otsubo Noriyuki
    • Journal Title

      canadian mathematical journal

      Volume: 70 (3) Issue: 3 Pages: 481-514

    • DOI

      10.4153/cjm-2017-008-6

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] CM periods, CM regulators and hypergeometric functions, II2017

    • Author(s)
      Asakura Masanori、Otsubo Noriyuki
    • Journal Title

      Mathematische Zeitschrift

      Volume: 印刷中 (published online) Issue: 3-4 Pages: 1325-1355

    • DOI

      10.1007/s00209-017-2001-1

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 超幾何微分方程式のJacobi標準形と変換公式2022

    • Author(s)
      大坪紀之
    • Organizer
      函数方程式論サマーセミナー
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 有限体上の超幾何関数2022

    • Author(s)
      大坪紀之
    • Organizer
      函数方程式論サマーセミナー
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 超幾何モチーフと種々の実現2022

    • Author(s)
      大坪紀之
    • Organizer
      函数方程式論サマーセミナー
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Hypergeometric motives and p-adic periods2022

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      p-adic Cohomology and Arithmetic Geometry 2022
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Gross-Deligne CM周期予想のl進類似とp進類似2022

    • Author(s)
      大坪紀之
    • Organizer
      代数的整数論とその周辺,
    • Related Report
      2022 Annual Research Report
  • [Presentation] 有限体上の超幾何関数について2021

    • Author(s)
      大坪紀之
    • Organizer
      早稲田大学整数論セミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] 有限体上の超幾何関数について2021

    • Author(s)
      大坪紀之
    • Organizer
      愛媛大学代数セミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Periodes et motifs CM de type abeien2020

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      Seminaire de theorie des nombres de l'IMJ-PRG
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Hypergeometric motives and p-adic periods2020

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      Monodromy and hypergeometric functions
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A new approach to hypergeometric transformation formulas2019

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      Sendai Workshop on Hypergeometric Series, Mahler Measures, and Multiple Zeta Values
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Invariants of CM motives of abelian type2019

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      The Asia-Australia Algebra Conference
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 超幾何関数の変換公式について2018

    • Author(s)
      大坪紀之
    • Organizer
      第12回玉原特殊多様体研究集会
    • Related Report
      2018 Research-status Report
  • [Remarks] Noriyuki Otsubo's Website

    • URL

      https://sites.google.com/view/noriyuki-otsubo/home

    • Related Report
      2022 Annual Research Report
  • [Remarks] Noriyuki Otsubo's Home Page

    • URL

      https://sites.google.com/view/noriyuki-otsubo

    • Related Report
      2021 Research-status Report
  • [Remarks] Researchmap

    • URL

      https://researchmap.jp/n-otsubo

    • Related Report
      2021 Research-status Report 2020 Research-status Report
  • [Remarks] Noriyuki Otsubo's Home Page

    • URL

      http://www.math.s.chiba-u.ac.jp/~otsubo/index.html

    • Related Report
      2020 Research-status Report 2019 Research-status Report 2018 Research-status Report
  • [Remarks] researchmap

    • URL

      https://researchmap.jp/n-otsubo

    • Related Report
      2019 Research-status Report
  • [Funded Workshop] L-functions and Motives in Niseko 20222022

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] Regulators in Niseko 20192019

    • Related Report
      2019 Research-status Report

URL: 

Published: 2018-04-23   Modified: 2024-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi