Graduate School of Science and Engineering（Science）
理工学専攻（数理科学）
日本語
Update date：2025/01/07
Professor
Hirano Miki

Job Achievement

  1. 理工学研究科長（理学部長）その他2020/04/01-2021/03/31
  2. データサイエンスセンター長その他2020/04/01-2022/03/31
  3. データサイエンスセンター長その他2022/04/01-2024/03/31

Research History

  1. 2015/04-2021/03Ehime UniversityFaculty of ScienceDean
  2. 2020/04-presentEhime UniversityCenter for Data ScienceDirector
  3. 2024/04-presentEhime University副学長
  4. 2024/04-presentEhime Universityデジタル情報人材育成機構副機構長

Education

  1. Keio University1989/041993/03
  2. The University of Tokyo1993/041998/03
  3. Keio University1993
  4. The University of Tokyo1998

Degree

  1. 修士(数理科学)東京大学1995/03
  2. 博士(数理科学)東京大学1998/03

Research Areas

Research Projects

  1. 次数2の非正則ジーゲル保型形式に対するフーリエ・ヤコビ展開の研究若手研究(B)Principal investigator
  2. 次数2のジーゲル保型形式に対するフーリエ・ヤコビ展開の定式化の研究若手研究(B)Principal investigator
  3. Study of Fourier-Jacobi expansions for Siegel modular forms of degree two and associated special functions若手研究(B)Principal investigator
  4. Study of Fourier-Jacobi type spherical functions for Siegel modular forms of degree two and its application若手研究(B)Principal investigator
  5. Study of Fourier-Jacobi type spherical functions for Siegel modular forms of degree two and its application基盤研究(C)Principal investigator
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Papers

  1. Archimedean zeta integrals for GL(3) × GL(2)2022/06Miki Hirano Taku Ishii Tadashi MiyazakiMemoirs of the American Mathematical Society278/ 1366, 1-136URLURL_2In this article, we give explicit formulas of archimedean Whittaker functions on $GL(3)$ and $GL(2)$. Moreover, we apply those to the calculation of archimedean zeta integrals for $GL(3)\times GL(2)$, and show that the zeta integral for appropriate Whittaker functions is equal to the associated $L$-factors.
  2. RAMANUJAN CAYLEY GRAPHS OF FROBENIUS GROUPS2016/12Miki Hirano Kohei Katata Yoshinori YamasakiBULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY94/ 3, 373-38310.1017/S0004972716000587URLURL_2CAMBRIDGE UNIV PRESSWe determine a bound for the valency in a family of dihedrants of twice odd prime orders which guarantees that the Cayley graphs are Ramanujan graphs. We take two families of Cayley graphs with the underlying dihedral group of order 2p: one is the family of all Cayley graphs and the other is the family of normal ones. In the normal case, which is easier, we discuss the problem for a wider class of groups, the Frobenius groups. The result for the family of all Cayley graphs is similar to that for circulants: the prime p is 'exceptional' if and only if it is represented by one of six specific quadratic polynomials.
  3. The archimedean zeta integrals for GL(3) x GL(2)2016/02Miki Hirano Taku Ishii Tadashi MiyazakiPROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES92/ 2, 27-32Research paper (scientific journal)10.3792/pjaa.92.27URLJAPAN ACADWe consider here the archimedean zeta integrals for GL(3) x GL(2) and show that the zeta integral for appropriate Whittaker functions is equal to the associated L-factor.
  4. Ramanujan circulant graphs and the conjecture of Hardy-Littlewood and Bateman-Horn2016Miki Hirano Kohei Katata Yoshinori YamasakiPreprintarXiv:1310.2130(MISC) Institution technical report and pre-print, etc.URLIn this paper, we determine the bound of the valency of the odd circulant graph which guarantees to be a Ramanujan graph for each fixed number of vertices. In almost of the cases, the bound coincides with the trivial bound, which comes from the trivial estimate of the largest non-trivial eigenvalue of the circulant graph. As exceptional cases, the bound in fact exceeds the trivial one by two. We then prove that such exceptionals occur only in the cases where the number of vertices has at most two prime factors and is represented by a quadratic polynomial in a finite family and, moreover, under the conjecture of Hardy-Littlewood and Bateman-Horn, exist infinitely many.
  5. 無限素点における $GL(3)\times GL(2)$ に関する局所ゼータ積分 (モジュラー形式と保型表現)2015/11平野 幹 石井 卓 宮崎 直数理解析研究所講究録1973京都大学
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Presentations

  1. Whittaker functions on GL(4,R) and archimedean Bump-Friedberg integralsZeta functions in Okinawa 20242024/11/09Oral presentation(general)
  2. Whittaker functions on GL(4,R) and archimedean Bump-Friedberg integrals新潟代数セミナー2024/07/26Oral presentation(general)
  3. Whittaker functions on GL(4,R) and archimedean zeta integralsRIMS conference "Automorphic form, automorphic L-functions and related topics"2022/01/25
  4. Remarks on Ramanujan circulants and dihedrants香川セミナー2018/05/26
  5. Ramanujan Cayley graphs and the conjecture of Hardy-Littlewood and Bateman-Horn概均質セミナー2017/12/02Oral presentation(general)
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Allotted Class

  1. 2024Introduction to Mathematics
  2. 2024Introduction to Mathematics
  3. 2024Introduction to Mathematics
  4. 2024Introduction to Resilience Studies
  5. 2024AlgebraⅢ
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Social Activities

  1. S.C.M.21定例会における講演2020/09/25
  2. 愛媛経済研究会2017/10
  3. 19th Autumn Workshop on Number Theory2016/11/02-2016/11/06
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Professional Memberships

  1. 日本数学会
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Committee Memberships

  1. 2024/03-present日本数学会代数学分科会評議員
  2. 2022/07-present日本数学会教育研究資金問題検討委員会委員
  3. 2016/04-present日本数学会代数学分科会運営委員
  4. 2016/04-2017/03日本数学会中国・四国支部 代議員
  5. 2008/04-present愛媛県高等学校教育研究会数学部会顧問
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