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Periods, congruence and special values of L functions for modular forms

Research Project

Project/Area Number 16H03919
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHokkaido University (2020, 2022)
Muroran Institute of Technology (2016-2019)

Principal Investigator

KATSURADA Hidenori  北海道大学, 理学研究院, 研究院研究員 (80133792)

Project Period (FY) 2016-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥13,260,000 (Direct Cost: ¥10,200,000、Indirect Cost: ¥3,060,000)
Fiscal Year 2020: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2019: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2018: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2017: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
KeywordsHermitian Ikeda lift / Kim-Yamauchi lift / period relation / Gross-Keating invariant / Siegel series / Harder conjecture / 周期 / Siegel級数 / Harder予想 / Period / Grosss-Leating invariant / 合同 / 特殊値 / Gross-Keating不変量 / L関数 / ジーゲル級数 / L関数 / 代数学 / L関数の特殊値 / リフト / 数論 / 保型形式
Outline of Final Research Achievements

1.We proved an adelic version of Ikeda's conjecture on the period of the Hermitian Ikeda lift. 2.We proposed a conjecture on the period of the Kim-Yamauchi lift, and proved it(joint work with H.H. Kim and T.Yamauchi). 3.We constructed a fundamental
theory of quadratic forms over non-archimedean local fields, and gave an explicit formula for the Siegel series of a quadratic form (joint work with T. Ikeda). 4.We reformulated Harder's conjecture, and proved it for some cases (joint work with H. Atobe, M. Chida, T.Ibukiyama and T.Yamauchi).

Academic Significance and Societal Importance of the Research Achievements

(1) ユニタリー群やE7型例外群の保型形式に関して重要な興味深い結果を与えるとともに,例外型Jordan代数の局所理論に新たな知見を加えた.(2) 局所体の2次形式の理論をdyadic, non-dyadicに限らず統一的に扱えるようになった.また,Siegel級数の明示的な公式はDuke-Imamoglu-Ikeda liftのフーリエ係数の評価やShimura多様体のサイクルの交差数に関するKudla programにも使われ,今後も大域的な応用が見込まれる.(3) Harder予想の新しい定式化はBergstroem-Farber-van-der-Geer予想等にも新たな知見を与える.

Report

(6 results)
  • 2022 Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • Research Products

    (54 results)

All 2025 2023 2022 2020 2019 2018 2017 2016

All Journal Article (28 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 25 results,  Open Access: 2 results,  Acknowledgement Compliant: 2 results) Presentation (26 results) (of which Int'l Joint Research: 7 results,  Invited: 24 results)

  • [Journal Article] An inductive formula for the Gross-Keating invariant of a quadratic form2025

    • Author(s)
      S. Cho, T. Ikeda, H. Katsurada, C. H. Lee and T. Yamauchi
    • Journal Title

      Tohoku Math. J.

      Volume: -

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Twisted Koecher-Maass series of the Ikeda type lift for the exceptional group of type E(7,3)2023

    • Author(s)
      Hidenori Katsurada and Henry H. Kim
    • Journal Title

      J. Number Theory

      Volume: 248 Pages: 140-171

    • DOI

      10.1016/j.jnt.2023.01.010

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Harder's conjecture I2023

    • Author(s)
      H. Atobe, M. Chida, T. Ibukiyama, H. Katsurada and T. Yamauchi
    • Journal Title

      J. Math. Soc. Japan

      Volume: -

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimates for the Fourier coefficients of the Duke-Imamoglu-Ikeda lift2023

    • Author(s)
      Tamotsu Ikeda and Hidenori Katsurada
    • Journal Title

      Forum Math.

      Volume: - Issue: 4 Pages: 975-990

    • DOI

      10.1515/forum-2022-0197

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An explicit formula for the Siegel series of a quadratic form over a non-archimedean local filed,2022

    • Author(s)
      T. Ikeda and H. Katsurada
    • Journal Title

      J. reine. angew. Math.

      Volume: 783 Issue: 783 Pages: 1-47

    • DOI

      10.1515/crelle-2021-0061

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Period of the Ikeda type lift for the exceptional group of type E7,3.2022

    • Author(s)
      Katsurada, Hidenori; Kim, Henry H.; Yamauchi, Takuya
    • Journal Title

      Mathematische Zeitschrift

      Volume: 302 Issue: 1 Pages: 559-588

    • DOI

      10.1007/s00209-022-03057-w

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Boundedness of denominators of special values of the $L$-functions for modular forms2022

    • Author(s)
      H. Katsurada
    • Journal Title

      Comment. Math. St. Pauli.

      Volume: 70 Pages: 29-48

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the local densitiies and the Gross-Keating invariant2020

    • Author(s)
      S. Cho, Ikeda, H. Katsurada
    • Journal Title

      Math. Zeit.

      Volume: -

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Congruence for the Klingen-Eisenstein series and Harder's conjecture2020

    • Author(s)
      H. Katsurada
    • Journal Title

      Report of Oberwolfach Workshop 'Modular forms'

      Volume: 57 Pages: 55-57

    • Related Report
      2019 Annual Research Report
  • [Journal Article] On the Gross Keating invariant of a Hermitian form over a non-archimedean locall field2019

    • Author(s)
      T. IKeda and H. Katsurada
    • Journal Title

      数理解析研究所講究録

      Volume: 2100 Pages: 141-150

    • Related Report
      2018 Annual Research Report
  • [Journal Article] On the Gross-Keating invariant of a quadratic form over a non-archimedean local field2018

    • Author(s)
      T. Ikeda and H. Katsurada
    • Journal Title

      American Journal of Mathematics

      Volume: 140 Pages: 1521-1565

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Gross-Keating invariant of a quadratic form over a non-archimedian local field2018

    • Author(s)
      T. Ikeda and H. Katsurada
    • Journal Title

      Amer. J. Math

      Volume: ー

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Prym varieties for the coverings of some singular plane curves2018

    • Author(s)
      Lubjana Beshaj and Takuya Yamauchi
    • Journal Title

      Manuscripta mathematica

      Volume: 未定 Issue: 1-2 Pages: 1-18

    • DOI

      10.1007/s00229-018-1018-z

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An equidistribution theorem for holomorphic Siegel modular forms for $GSp_4$2018

    • Author(s)
      Henry H. Kim, S. Wakatsuki and T. Yamauchi
    • Journal Title

      Journal of the Institute of Mathematics of Jussieu

      Volume: -

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the period of the Ikeda lift for U(m,m)2017

    • Author(s)
      Katsurada Hidenori
    • Journal Title

      Mathematische Zeitschrift

      Volume: 286 Issue: 1-2 Pages: 141-178

    • DOI

      10.1007/s00209-016-1758-y

    • NAID

      120006459667

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Period of the adelic Ikeda lift for U(m,m)2017

    • Author(s)
      Katsurada Hidenori
    • Journal Title

      Abhandlungen Math. Seminar Univ. Hamburg

      Volume: - Issue: 1 Pages: 67-86

    • DOI

      10.1007/s12188-017-0178-1

    • NAID

      120006407255

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Explicit formula for the Siegel series of a quadratic form over a non-archimedean local field2017

    • Author(s)
      池田保,桂田英典
    • Journal Title

      数理解析研究所講究録

      Volume: 1777 Pages: 183-195

    • Related Report
      2017 Annual Research Report
  • [Journal Article] A Miyawaki type lift for GSpin(2,10)2017

    • Author(s)
      Henry H. Kim and T. Yamauchi
    • Journal Title

      Math zeitschlift

      Volume: 288 Pages: 415-437

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Selmer groups and central values of L-functions for modular forms2017

    • Author(s)
      Masataka Chida
    • Journal Title

      Annales de l'Institut Fourier

      Volume: 67 Issue: 3 Pages: 1231-1276

    • DOI

      10.5802/aif.3108

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Period of the adelic Ikeda lift for U(m,m)2017

    • Author(s)
      H. Katsurada
    • Journal Title

      Abhand. Math. Semin. Univ. Hamburg

      Volume: 印刷中

    • NAID

      120006407255

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Eisenstien congruences for SO(4,3), SO(4,4), spinor, and triple product L-values2017

    • Author(s)
      J. Bergstrom, N. Dummigan, T. Ibukiyama and H. Katsurada
    • Journal Title

      Experimental Math.

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the functional equation of the Siegel series2017

    • Author(s)
      T. Ikeda
    • Journal Title

      J. Number Theory

      Volume: 172 Pages: 44-62

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A uniform structure on subgroups of GL_n(F_q) and its application to a conditional construction of Artin representations of GL_n2017

    • Author(s)
      H. H. Kim and T. Yamauchi
    • Journal Title

      J. Ramanujan Math. Soc.

      Volume: 32 Pages: 75-99

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Selmer groups and central values of L-functions fo modular forms2017

    • Author(s)
      M. Chida
    • Journal Title

      Anales de l'Institut Fourer

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Notes on theta series for Niemeier lattices2017

    • Author(s)
      S. Nagaoka and S. Takemori
    • Journal Title

      Ramanujan J.

      Volume: 42 Issue: 2 Pages: 385-400

    • DOI

      10.1007/s11139-015-9720-x

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eisenstein congruences for SO(4,3) and SO(4,4), spinor and triple products L values2016

    • Author(s)
      J. Bergstoem, N. Dummigan, T. Megarbane, T. Ibukiyama, H. Katsurada,
    • Journal Title

      Experimental Mathematics(Published Online)

      Volume: 23 Dec Issue: 2 Pages: 1-21

    • DOI

      10.1080/10586458.2016.1251861

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On intermediate Jacobians of cube threefolds admitting an automorphism of order five2016

    • Author(s)
      B. van Geeman and T. Yamauchi
    • Journal Title

      Pure Appl. Math. Q.

      Volume: 12 Pages: 141-164

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Structure theorems for vector valued Siegel modular forms of degree 2 and weight det^k x Sym(10)2016

    • Author(s)
      S. Takemori
    • Journal Title

      International J. Math.

      Volume: 27

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Presentation] Congruence between certain lifts and Harder's conjecture2023

    • Author(s)
      Hidenori Katsurada
    • Organizer
      保型形式と数論
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Estimates for Fourier coefficients of the Duke-Imamoglu-Ikeda lift 2022年6月24日 京都2022

    • Author(s)
      桂田英典,
    • Organizer
      9th Kyoto conference on automorphic forms,
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Explicit formulas for the Rankin-Selberg series of the Ikeda type lifts and their application to the quantum unique ergodicity2022

    • Author(s)
      Hidenori Katsurada
    • Organizer
      23rd Autumn Workshop on Number Theory
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Congruence for the Klingen-Eisenstein lift and Harder's conjecture2019

    • Author(s)
      Hidenori Katsurada
    • Organizer
      22-th Hakuba Autumn Workshop
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Congruence for the Klinegen-Eisenstein seires and Harder's conjecture2019

    • Author(s)
      HIdenori Katsurada
    • Organizer
      Oberwolfach Workshop 'Modular forms'
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Gross-Keating invariant for Hermitian forms,2018

    • Author(s)
      池田保、桂田英典
    • Organizer
      RIMS 共同研究(公開型) 保型形式の解析的・数論的研究
    • Related Report
      2017 Annual Research Report
  • [Presentation] The weight part of Serre conjecture for GSp4/Q in terms of the classical weights2018

    • Author(s)
      T. Yamauchi
    • Organizer
      Galois representations, ramification theory, and related topics
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Arithmetic diagonal cycles and special values of p-adic L-functions2018

    • Author(s)
      Masataka Chida
    • Organizer
      UK-Japan Winter School 2018 ``Galois Representations and Automorphic forms'
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Pullback of Eisenstein series and its applications (1),(2) ,2017

    • Author(s)
      H. Katsurada,
    • Organizer
      The 20th Hakuba Workshop
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Explicit formula for Siegel series2017

    • Author(s)
      H. Katsurada,
    • Organizer
      Number Theory Down Under
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 高次代数群に対する保型形式とその周辺2017

    • Author(s)
      山内卓也
    • Organizer
      代数学シンポジウム
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Chow-Heegner cycles on products of CM elliptic curves2017

    • Author(s)
      Masataka Chida
    • Organizer
      Fukuoka International Conference on Arithmetic Geometry in 2017
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Chow-Heegner cycles on self-products of CM elliptic curves2017

    • Author(s)
      Masataka Chida
    • Organizer
      Workshop on p-adic L-functions and algebraic cycles
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] An equidistribution theorem for holomorphic Siegel modular forms for GSp_42017

    • Author(s)
      山内卓也
    • Organizer
      京都大学RIMS研究集会「保型形式とその周辺」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Construction of theta functions of any vector valued weight2017

    • Author(s)
      竹森翔
    • Organizer
      京都大学RIMS研究集会「保型形式とその周辺」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] An explicit formula for the Siegel series2016

    • Author(s)
      桂田英典
    • Organizer
      東北大学代数学セミナー
    • Place of Presentation
      東北大学(宮城県)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Period and congruence of automorphic form,2016

    • Author(s)
      H. Katsurada
    • Organizer
      Number Theory Down Under
    • Place of Presentation
      Newcastle(Australia)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Gross-Keating invariant of a quadractic form over a non-archimedean local field of characteristic zero and its application to Siegel series2016

    • Author(s)
      T. Ikeda
    • Organizer
      Pan Asia Number Theory conference
    • Place of Presentation
      台湾国立大学(台湾)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Kohnen plus space for Hilbert modular forms2016

    • Author(s)
      T. Ikeda
    • Organizer
      International Conference for the 70th Anniversary of Korean Mathematical Society2016 KMS Annual Meeting
    • Place of Presentation
      ソウル大学(韓国)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Arthur-Selberg trace formulaとその応用2016

    • Author(s)
      山内卓也
    • Organizer
      東北代数学セミナー
    • Place of Presentation
      東北大学(宮城県)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] GSp4に関するセール予想と重さ還元定理2016

    • Author(s)
      山内卓也
    • Organizer
      日本数学会代数学特別講演
    • Place of Presentation
      関西大学(大阪府)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] A survey for Ikeda type constructions of holomorphic automorphic cusp forms of level one2016

    • Author(s)
      T. Yamauchi
    • Organizer
      台北(台湾)・国立大学数論セミナー
    • Place of Presentation
      台北(台湾)・国立大学(台湾)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Ikeda type lift for E_{7,3} /Q2016

    • Author(s)
      T Yamauchi
    • Organizer
      台北(台湾)・国立大学数論セミナー
    • Place of Presentation
      台北(台湾)・国立大学(台湾)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] モチーフの円分p進L関数の存在予想2016

    • Author(s)
      千田雅隆
    • Organizer
      保型L関数の特殊値と付随するp進L関数
    • Place of Presentation
      美山町自然文化村 河鹿荘(京都府)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Selmer groups for Rankin-Selberg products of modular forms2016

    • Author(s)
      M. Chida
    • Organizer
      p-adic methods and in arithmetic geometry at Sendai
    • Place of Presentation
      東北大学片平キャンパス 知の館(京都府)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Theta operators on mod p Siegel modular forms2016

    • Author(s)
      竹森翔
    • Organizer
      p進保型形式,p進ガロア表現と関連する話題
    • Place of Presentation
      佐賀大学(佐賀県)
    • Related Report
      2016 Annual Research Report
    • Invited

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Published: 2016-04-21   Modified: 2024-01-30  

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