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Research on distributions of prime geodesics and spectrum using trace formula and zeta functions

Research Project

Project/Area Number 17K05181
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionUniversity of the Ryukyus

Principal Investigator

Hashimoto Yasufumi  琉球大学, 理学部, 准教授 (30452733)

Project Period (FY) 2017-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsセルバーグ跡公式 / セルバーグゼータ関数 / 双曲多様体 / length spectrum / ラプラシアンのスペクトル / 跡公式 / 普遍性定理 / 素測地線定理 / 2次形式の類数 / ゼータ関数 / 素測地線 / スペクトル
Outline of Final Research Achievements

There are deep connections between the distributions of the spectra of the Laplacian and the prime geodesics of hyperbolic manifolds of finite volume derived from discrete subgroups of a semi-simple Lie group of real rank one. The aim of this study is to characterize the corresponding manifolds by studying the two distributions in relation to each other using Selberg's trace formula. During the course of this study, we evaluated the values of the Selberg zeta functions in the non-absolute convergence region for various arithmetic groups, including congruence subgroups and co-compact groups derived from indefinite quaternion algebras. We also generalized and extended the universality theorems of the Selberg zeta function from existing researches.

Academic Significance and Societal Importance of the Research Achievements

セルバーグゼータ関数については、リーマンゼータ関数との類似性が強調されることが多いが、有理型関数としての位数や非自明零点の分布、素元の分布などで大きな相違があるため、従来の解析数論的な手法では解析が必ずしも簡単ではないことが少なくない。本研究では、既知のセルバーグゼータ関数の値の評価や、値分布の普遍性に関する結果を改良することで、この研究分野における素元の分布を丁寧に解析することの重要性の一端に触れることができたと考える。

Report

(7 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
  • 2017 Research-status Report
  • Research Products

    (41 results)

All 2023 2022 2021 2020 2019 2018 2017

All Journal Article (20 results) (of which Peer Reviewed: 16 results,  Open Access: 12 results,  Acknowledgement Compliant: 2 results) Presentation (21 results) (of which Int'l Joint Research: 3 results)

  • [Journal Article] Solving the Problem of Blockwise Isomorphism of Polynomials with Circulant Matrices2023

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E106.A Issue: 3 Pages: 185-192

    • DOI

      10.1587/transfun.2022CIP0002

    • ISSN
      0916-8508, 1745-1337
    • Year and Date
      2023-03-01
    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Square integrals of the logarithmic derivatives of Selberg’s zeta functions in the critical strip2023

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      International Journal of Number Theor

      Volume: 19 Issue: 04 Pages: 747-756

    • DOI

      10.1142/s1793042123500379

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Key recovery attack on Hufu-UOV2022

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      JSIAM Letters

      Volume: 14 Issue: 0 Pages: 1-4

    • DOI

      10.14495/jsiaml.14.1

    • NAID

      130008145019

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2022 Annual Research Report 2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Selberg's zeta function for the modular group in the critical strip2021

    • Author(s)
      Hashimoto Yasufumi
    • Journal Title

      Mathematische Nachrichten

      Volume: 294 Issue: 10 Pages: 1899-1904

    • DOI

      10.1002/mana.202000268

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Solving the Problem of Blockwise Isomorphism of Polynomials with Circulant Matrices2021

    • Author(s)
      Hashimoto Yasufumi
    • Journal Title

      Springer LNCS

      Volume: 12835 Pages: 137-150

    • DOI

      10.1007/978-3-030-85987-9_8

    • ISBN
      9783030859862, 9783030859879
    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Vulnerability of Diene-Thabet-Yusuf's cubic multivariate signature scheme,2021

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      Ryukyu Mathematical Journal

      Volume: 34 Pages: 1-5

    • NAID

      120007182128

    • Related Report
      2021 Research-status Report
    • Open Access
  • [Journal Article] Selberg's zeta function for the modular group in the critical strip2021

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      Mathematische Nachrichten

      Volume: 未定

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Recent Developments in Multivariate Public Key Cryptosystems2020

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      International Symposium on Mathematics, Quantum Theory, and Cryptography

      Volume: - Pages: 209-229

    • DOI

      10.1007/978-981-15-5191-8_16

    • ISBN
      9789811551901, 9789811551918
    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Asymptotic behaviors of class number sums associated with Pell-type equations2019

    • Author(s)
      Y. Hashimoto
    • Journal Title

      Mathematische Zeitschrift

      Volume: 292 Issue: 1-2 Pages: 641-654

    • DOI

      10.1007/s00209-018-2139-5

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Key recovery attack on Circulant UOV/Rainbow2019

    • Author(s)
      Y. Hashimoto
    • Journal Title

      JSIAM Letters

      Volume: 11 Issue: 0 Pages: 45-48

    • DOI

      10.14495/jsiaml.11.45

    • NAID

      130007696300

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Chosen Message Attack on Multivariate Signature ELSA at Asiacrypt 20172019

    • Author(s)
      Y. Hashimoto, Y. Ikematsu, T. Takagi
    • Journal Title

      Journal of Information Processing

      Volume: 27 Issue: 0 Pages: 517-524

    • DOI

      10.2197/ipsjjip.27.517

    • NAID

      130007706936

    • ISSN
      1882-6652
    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Recent developments in multivariate public key cryptosystems2019

    • Author(s)
      Y. Hashimoto
    • Journal Title

      MI Lecture Notes

      Volume: 81 Pages: 187-205

    • Related Report
      2019 Research-status Report
  • [Journal Article] Chosen Message Attack on Multivariate Signature ELSA at Asiacrypt 20172019

    • Author(s)
      Y. Hashimoto, Y. Ikematsu, T. Takagi
    • Journal Title

      IPSJ Journal

      Volume: 印刷中

    • NAID

      130007706936

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] High-rank attack on HMFEv2018

    • Author(s)
      Y. Hashimoto
    • Journal Title

      JSIAM Letters

      Volume: 10 Issue: 0 Pages: 21-24

    • DOI

      10.14495/jsiaml.10.21

    • NAID

      130007404541

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Chosen Message Attack on Multivariate Signature ELSA at Asiacrypt 20172018

    • Author(s)
      Y. Hashimoto, Y. Ikematsu, T. Takagi
    • Journal Title

      Springer LNCS

      Volume: 11049 Pages: 3-18

    • DOI

      10.1007/978-3-319-97916-8_1

    • NAID

      130007706936

    • ISBN
      9783319979151, 9783319979168
    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the security of Zhang-Tan's variants of multivariate signature schemes2018

    • Author(s)
      Y. Hashimoto
    • Journal Title

      Ryukyu Mathematical Journal

      Volume: 31 Pages: 1-5

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] Multivariate public key cryptosystems2017

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      Mathematical Modelling for Next-Generation Cryptography

      Volume: 1 Pages: 17-42

    • DOI

      10.1007/978-981-10-5065-7_2

    • ISBN
      9789811050640, 9789811050657
    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Chosen ciphertext attack on ZHFE2017

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      JSIAM Letters

      Volume: 9 Issue: 0 Pages: 21-24

    • DOI

      10.14495/jsiaml.9.21

    • NAID

      130005540822

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Key Recovery Attacks on Multivariate Public Key Cryptosystems Derived from Quadratic Forms over an Extension Field2017

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E100.A Issue: 1 Pages: 18-25

    • DOI

      10.1587/transfun.E100.A.18

    • NAID

      130005180815

    • ISSN
      0916-8508, 1745-1337
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Weaknesses of cubic UOV and its variants2017

    • Author(s)
      Yasufumi Hashimoto
    • Journal Title

      Ryukyu mathematical journal

      Volume: 30 Pages: 1-7

    • NAID

      120006378227

    • Related Report
      2017 Research-status Report
    • Open Access
  • [Presentation] セルバーグゼータ関数に関する普遍性定理2023

    • Author(s)
      橋本康史
    • Organizer
      2023年度日本数学会年会代数学分科会
    • Related Report
      2022 Annual Research Report
  • [Presentation] 有限体上の under-defined な多変数連立2次方程式の解法について2023

    • Author(s)
      橋本康史
    • Organizer
      日本応用数理学会第19回研究部会連合発表会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Universality of the Selberg zeta function2022

    • Author(s)
      Yasufumi Hashimoto
    • Organizer
      Zeta Functions in OKINAWA 2022
    • Related Report
      2022 Annual Research Report
  • [Presentation] Simple matrix signature scheme の安全性について2022

    • Author(s)
      橋本康史
    • Organizer
      日本応用数理学会第18回研究部会連合発表会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Solving the problem of Blockwise Isomorphism of Polynomials with Circulant matrice2021

    • Author(s)
      Yasufumi Hashimoto
    • Organizer
      16th International Workshop on Security (IWSEC2021)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] セルバーグゼータ関数の臨界領域における2乗積分について2021

    • Author(s)
      橋本康史
    • Organizer
      2021年度日本数学会秋季総合分科会
    • Related Report
      2021 Research-status Report
  • [Presentation] Hufu-UOVの安全性について2021

    • Author(s)
      橋本康史
    • Organizer
      日本応用数理学会年会第17回研究部会連合発表会
    • Related Report
      2021 Research-status Report
  • [Presentation] モジュラー群に関するセルバーグゼータ関数の臨界領域での値について2020

    • Author(s)
      橋本康史
    • Organizer
      2020年度日本数学会秋季総合分科会代数学分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] Diene-Thabet-Yusuf の3次多変数署名方式の安全性について2020

    • Author(s)
      橋本康史
    • Organizer
      2020年度日本応用数理学会年会
    • Related Report
      2020 Research-status Report
  • [Presentation] Recent developments in multivariate public key cryptosystems2019

    • Author(s)
      Y. Hashimoto
    • Organizer
      International Symposium on Mathematics, Quantum Theory, and Cryptography
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] An error term estimation of the prime geodesic theorem for the modular group2019

    • Author(s)
      Y. Hashimoto
    • Organizer
      Zeta Functions in OKINAWA 2019
    • Related Report
      2019 Research-status Report
  • [Presentation] On multiplicities of eigenvalues of Laplacians on hyperbolic surfaces2018

    • Author(s)
      Y. Hashimoto
    • Organizer
      Zeta Functions in OKINAWA 2018
    • Related Report
      2018 Research-status Report
  • [Presentation] Chosen Message Attack on Multivariate Signature ELSA at Asiacrypt 20172018

    • Author(s)
      Y. Hashimoto, Y. Ikematsu, T. Takagi
    • Organizer
      The 13th International Workshop on Security (IWSEC 2018)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Circulant UOV/Rainbow の安全性について2018

    • Author(s)
      橋本康史
    • Organizer
      2018年度日本応用数理学会年会
    • Related Report
      2018 Research-status Report
  • [Presentation] A survey on Multivariate Public key Cryptosystem2018

    • Author(s)
      橋本康史
    • Organizer
      代数的手法による数理暗号解析
    • Related Report
      2018 Research-status Report
  • [Presentation] 多変数多項式暗号の暗号化の効率化2018

    • Author(s)
      橋本康史
    • Organizer
      2018年度暗号と情報セキュリティシンポジウム
    • Related Report
      2017 Research-status Report
  • [Presentation] A survey on multivariate public key cryptosystem2018

    • Author(s)
      橋本康史
    • Organizer
      代数的手法による数理暗号解析
    • Related Report
      2017 Research-status Report
  • [Presentation] Multiplicities in length spectra for congruence subgroups2017

    • Author(s)
      Yasufumi Hashimoto
    • Organizer
      Zeta functions and trace formulas in Fukuoka
    • Related Report
      2017 Research-status Report
  • [Presentation] Multiplicities in length spectra for non-compact arithmetic surfaces2017

    • Author(s)
      Yasufumi Hashimoto
    • Organizer
      Zeta Functions in OKINAWA 2017
    • Related Report
      2017 Research-status Report
  • [Presentation] HMFEv の安全性について2017

    • Author(s)
      橋本康史
    • Organizer
      日本応用数理学会2017年度年会
    • Related Report
      2017 Research-status Report
  • [Presentation] 拡大体型多変数多項式暗号に対するランク攻撃2017

    • Author(s)
      橋本康史
    • Organizer
      CREST暗号数理 平成29年度第2回全体会議
    • Related Report
      2017 Research-status Report

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Published: 2017-04-28   Modified: 2024-01-30  

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