Organization
Graduate School of Science and Engineering (Science) Major of Science and Engineering Mathematics and Computer Science Professor
Title
Professor
Contact information
External link
Hirano Miki
Degree
-
博士(数理科学) ( 1998.3 東京大学 )
-
修士(数理科学) ( 1995.3 東京大学 )
Research Areas
-
Natural Science / Algebra
Education
-
The University of Tokyo Graduate School of Mathematical Sciences
1993.4 - 1998.3
Country： Japan
-
Keio University Faculty of Science and Technology Department of Mathematics
1989.4 - 1993.3
Country： Japan
Research History
-
Ehime University Vice President
2024.4
-
Ehime University Associate Director
2024.4
-
Ehime University Center for Data Science Director
2020.4
-
Ehime University Faculty of Science Dean
2015.4 - 2021.3
Professional Memberships
-
日本数学会
Committee Memberships
-
日本数学会 代数学分科会評議員
2024.3
-
日本数学会 教育研究資金問題検討委員会委員
2022.7
Committee type：Academic society
-
日本数学会 代数学分科会運営委員
2016.4
Committee type：Academic society
-
日本数学会 中国・四国支部 代議員
2016.4 - 2017.3
Committee type：Academic society
-
愛媛県高等学校教育研究会 数学部会顧問
2008.4
Committee type：Municipal
-
愛媛県スーパーサイエンスハイスクール運営指導委員会 運営指導委員
2008.4
Committee type：Municipal
-
日本数学会 「数学」非常任編集委員
2002 - 2005
Papers
-
Archimedean zeta integrals for GL(3) × GL(2) Reviewed
Miki Hirano, Taku Ishii, Tadashi Miyazaki
Memoirs of the American Mathematical Society 278 ( 1366 ) 1 - 136 2022.6
-
RAMANUJAN CAYLEY GRAPHS OF FROBENIUS GROUPS Reviewed
Miki Hirano, Kohei Katata, Yoshinori Yamasaki
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 94 ( 3 ) 373 - 383 2016.12
-
The archimedean zeta integrals for GL(3) x GL(2) Reviewed
Miki Hirano, Taku Ishii, Tadashi Miyazaki
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 92 ( 2 ) 27 - 32 2016.2
-
The archimedean Whittaker functions on GL(3) Reviewed
Miki Hirano, Taku Ishii, Tadashi Miyazaki
GEOMETRY AND ANALYSIS OF AUTOMORPHIC FORMS OF SEVERAL VARIABLES 7 77 - 109 2012
-
Jackson q-Mahler measures Reviewed
Miki Hirano, Nobushige Kurokawa
Functiones et Approximatio, Commentarii Mathematici 42 ( 1 ) 51 - 58 2010
-
Calculus of principal series Whittaker functions on GL(3, C) Reviewed
Miki Hirano, Takayuki Oda
JOURNAL OF FUNCTIONAL ANALYSIS 256 ( 7 ) 2222 - 2267 2009.4
-
Whittaker functions for P-j-principal series representations of Sp(3, R) Reviewed
Miki Hirano, Taku Ishii, Takayuki Oda
ADVANCES IN MATHEMATICS 215 ( 2 ) 734 - 765 2007.11
-
Confluence from Siegel-Whittaker functions to Whittaker functions on Sp(2, R) Reviewed
Miki Hirano, Taku Ishii, Takayuki Oda
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY 141 15 - 31 2006.7
-
Secondary Whittaker functions for P-J-principal series representations of Sp(3, R) Reviewed
M Hirano, T Oda
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 81 ( 6 ) 105 - 109 2005.6
-
Fourier-Jacobi type spherical functions for principal series representations of Sp(2, R) Reviewed
Miki Hirano
Indagationes Mathematicae 15 ( 1 ) 43 - 54 2004
-
Half zeta functions Reviewed
HIRANO Miki, KUROKAWA Nobushige, WAKAYAMA Masato
J. Ramanujan Math. Soc. 18 ( 2 ) 195 - 209 2003
-
Fourier-Jacobi type spherical, functions for P-j-principal series representations of Sp(2,R) Reviewed
M Hirano
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES 65 524 - 546 2002.6
-
Fourier-Jacobi type spherical functions for discrete series representations of Sp(2, R) Reviewed
M Hirano
COMPOSITIO MATHEMATICA 128 ( 2 ) 177 - 216 2001
-
Shintani functions on GL(2, C) Reviewed
M Hirano
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 353 ( 4 ) 1535 - 1550 2001
-
Shintani functions on GL(2; R) Reviewed
M Hirano
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 352 ( 4 ) 1709 - 1721 2000
-
On theta type functions associated with the zeros of the Selberg zeta functions Reviewed
M Hirano
MANUSCRIPTA MATHEMATICA 92 ( 1 ) 87 - 105 1997.1
-
ON CARTIER-VOROS TYPE SELBERG TRACE FORMULA FOR CONGRUENCE SUBGROUPS OF PSL(2,R) Reviewed
M HIRANO
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 71 ( 7 ) 144 - 147 1995.9
MISC
-
Whittaker functions on GL(4,R) and archimedean Bump--Friedberg integrals
Miki Hirano, Taku Ishii, Tadashi Miyazaki
preprint 2024.8
-
Ramanujan circulant graphs and the conjecture of Hardy-Littlewood and Bateman-Horn
Miki Hirano, Kohei Katata, Yoshinori Yamasaki
Preprint arXiv:1310.2130 2016
-
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)
平野 幹, 石井 卓, 宮崎 直
数理解析研究所講究録 1973 101 - 114 2015.11
-
PRINCIPAL SERIES WHITTAKER FUNCTIONS ON $GL$(3, C) (Automorphic Representations, Automorphic Forms, L-functions, and Related Topics)
HIRANO MIKI, ODA TAKAYUKI
RIMS Kokyuroku 1617 178 - 186 2008.10
-
PROPAGATION FORMULA FOR PRINCIPAL SERIES WHITTAKER FUNCTIONS ON GL(3,C)
Hirano Miki
Journal of the Faculty of Science and Technology Seikei University 44 ( 2 ) 17 - 23 2007.12
-
Confluence from Siegel-Whittaker functions to Whittaker functions on $Sp$(2, $\mathbf{R}$) (Automorphic forms on $Sp$(2,$\mathbf{R}$) and $SU$(2,2) III)
Hirano Miki, Ishii Taku, Oda Takayuki
RIMS Kokyuroku 1421 72 - 84 2005.4
-
WHITTAKER FUNCTIONS FOR $P_J$-PRINCIPAL SERIES REPRESENTATIONS OF $Sp$(3, $\mathbf{R}$) (Automorphic forms on $Sp$(2,$\mathbf{R}$) and $SU$(2,2) III)
Hirano Miki, Oda Takayuki
RIMS Kokyuroku 1421 55 - 64 2005.4
-
Archimedean Shintani functions on $GL(2)$ (Automorphic Forms and $L$-Functions)
Hirano Miki
RIMS Kokyuroku 1103 1 - 7 1999.6
-
$GL$(2,$\mathbf{C}$)上の新谷関数 (Sp(2;$\mathbb{R}$)とSU(2,2)上の保型形式 II)
平野 幹
数理解析研究所講究録 1094 88 - 96 1999.4
-
FOURIER-JACOBI TYPE SPHERICAL FUNCTIONS ON $S_p(2,\mathbf{R})$ ; THE CASE OF $P_J$-PRINCIPAL SERIES AND DISCRETE SERIES (Automorphic Forms and Number Theory)
Hirano Miki
RIMS Kokyuroku 1052 10 - 18 1998.6
Presentations
-
Explicit archimedean Whittaker functions
Hirano, Miki
2025.2
-
Whittaker functions on GL(4,R) and archimedean zeta integrals
Miki Hirano, Taku Ishii, Tadashi Miyazaki
RIMS conference "Automorphic form, automorphic L-functions and related topics" 2022.1
-
Fourier-Jacobi models on Sp_2(R) International conference
HIRANO Miki
19th Autumn Workshop on Number Theory 2016.11
-
Remarks on Ramanujan circulants and dihedrants
HIRANO Miki
2018.5
-
Whittaker functions on GL(4,R) and archimedean Bump-Friedberg integrals
Miki Hirano
Zeta functions in Okinawa 2024 2024.11
-
Whittaker functions on GL(4,R) and archimedean Bump-Friedberg integrals
平野 幹
新潟代数セミナー 2024.7
-
Ramanujan Cayley graphs and the conjecture of Hardy-Littlewood and Bateman-Horn
HIRANO Miki
2017.12
Research Projects
-
グラフ上の調和解析の視点による整数論の研究
2019.4 - 2024.3
日本学術振興会 科学研究費助成事業 基盤研究(C) 基盤研究(C)
平野 幹
Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）
今年度も昨年度に引き続き、代数的に定義された有限正則グラフに対する明示的調和解析を整数論の観点で考察するための基礎的な考察を行った。とりわけ、保型形式論の観点から特殊関数の有限型類似物について考察した。
<BR>
有限体上の簡約可能群および関連する対称空間に付随する有限正則グラフ上の調和解析を整数論の観点で考察するためには、指数関数や超幾何型関数、ガンマ関数といった、通常の調和解析や整数論に現れる特殊関数の有限型類似物についての理解が不可欠である。これらの特殊関数の有限型類似物はこれまでにも豊富に考察されているが、今年度は、有限体上の代数群上の調和解析について、とりわけ表現の記述の視点から考察することに加え、有限特殊関数の研究状況について情報収集した。とりわけ、特定のゲルファント対に関連する球関数を特殊関数として明示的に記述することは、そのゲルファント対から得られる対称空間上の調和解析に基づく整数論的考察において肝要である。有限体上の代数群に対するゲルファント対の研究は非常に多くみられるが、有限特殊関数の詳細な研究とその整数論への応用の観点から整理されたものはあまり多くないように思われる。これらについて散見される事実を整理することにより、本研究課題であるグラフ上の調和解析の視点による整数論の研究に向けた基盤整備を進めているところである。
<BR>
今後は、これまでの３年間の研究により得た整数論と関連する有限型特殊関数についての知見をさらに深めると同時に、これらを活用して整数論的視点による有限体上の簡約可能群および関連する対称空間に付随する有限正則グラフ上の調和解析の明示的研究を進める予定である。また、ラマヌジャングラフについての研究にも着手したいと考えている。 -
ジェンダー・地域格差に配慮したSTEAM才能教育カリキュラムに関する学際的研究
2017.4 - 2021.3
日本学術振興会 科学研究費補助金 基盤研究(A)
隅田 学
Grant type：Competitive
-
有限対称空間および関連するグラフスペクトル論の視点による整数論の研究
2016.4 - 2019.3
日本学術振興会 科学研究費補助金 挑戦的萌芽研究
平野 幹
Authorship：Principal investigator Grant type：Competitive
-
次数２のジーゲル保型形式に対するフーリエ・ヤコビ型球関数の研究とその応用
2012.4 - 2015.3
日本学術振興会 科学研究費補助金 基盤研究(C)
平野 幹
Authorship：Principal investigator Grant type：Competitive
-
Arithmetic study of automorphic forms of many variables by various method
2011.4 - 2015.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)
ODA Takayuki, HIRONAKA Yumiko, WAKATSUKI Satoshi, KOSEKI Harutaka, HAYATA Takahiro, TSUZUKI Masao, HIRANO Miki, GON Yasuro, ISHI Taku
Grant amount：\30810000 （ Direct Cost: \23700000 、 Indirect Cost：\7110000 ）
We obtained some fundamental results on the integral expressions and power series expressions of the A-radial parts of either Whittaker functions or spherical functions for the standard representations (i.e principal series and/or discrete series representations) of the Lie groups, GL(n,R), Sp(2,R) and SU(3,1).The formulas of Whittaker functions of non-spherical principal series put a period on the research history beginning from the studies of D. Bump and others, and we can expect various applications of this result (this is a joint works with Taku Ishii of Seikei Univ.). We obtained an explicit formulas of the matrix coefficients of the large discrete series of the Lie groups SU(2,1), SU(3,1) (joint wrok with T.Hayata, H. Koseki, and T. Miyazaki).This result gives a suggestion for study of the reproducing kernels. We push forward the investigation oh the cell-decomposition of Siegel-Gottschling fundamental domain of genus 2 (the first paper was a joint paper with T. Hayata).
-
次数2のジーゲル保型形式に対するフーリエ・ヤコビ型球関数とその応用
2009.4 - 2012.3
日本学術振興会 科学研究費補助金 若手研究(B)
平野 幹
Authorship：Principal investigator Grant type：Competitive
-
Analysis, geometry and arithmetic of automorphic forms of many variables and higher dimensional modular varieties
2007 - 2010
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)
ODA Takayuki, ISHII Taku, ICHIKAWA Takashi, IBUKIYAMA Tomoyoshi, ARIYAMA Kazutoshi, KOSEKI Harutaka, SATO Fumihiro, SUGANO Takashi, TSUZUKI Masao, HAYATA Takahiro, HAMAHATA Yoshinori, HIRANO Miki, HIRONAKA Yumiko, MURASE Atsushi, WATANABE Takao
Grant amount：\40950000 （ Direct Cost: \31500000 、 Indirect Cost：\9450000 ）
About matrix coefficients of semi-simple Lie groups, we obtained a more precise result for the middle discrete series of SU(2, 2) about the asymptotic expansion. We investigated the explicit formula of the matrix coefficients of SU(3, 1)(both are joint works together with T. Hayata and H. Koseki). Utilizing the asymptotic expansion, we obtained the explicit formula of the c-functions of certain P_J-principal series representations of Sp(2, R) explicitly(joint work with M. Iida). We push forward the investigation of 0-cells of the fundamental domain of the Siegel modular group of genus 2.
-
次数2のジーゲル保型形式に対するフーリエ・ヤコビ展開と関連する特殊関数の研究
2006.4 - 2009.3
日本学術振興会 科学研究費補助金 若手研究(B)
平野 幹
Authorship：Principal investigator Grant type：Competitive
-
Cohomology Theory of Finite Groups
2005 - 2007
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
SASAKI Hiroki, WATANABE Atumi, SANADA Katsunori, KAWAI Hiroaki, NIWASAKI Takashi
Grant amount：\3730000 （ Direct Cost: \3400000 、 Indirect Cost：\330000 ）
Many problems of fundamental importance are left unsolved in the theory of cohomology of block ideals of finite groups. Let G be a finite groups and k an algebraically closed field of prime characteristic dividing the order of G. Let B be a block ideal of kG and let D be a defect group. Let P be a subgroup of D and let H be a subgroup of G containing DC _G (D) and N_G (P). Assume that a block ideal C of kH and the block B are in Brauer correspondence and D is also a defect group of C. It is significantly important to investigate relationships between the block cohomologies H^* (G, B) and H^* (H,C). For example, when H^* (G, B) ⊆ H^* (H,C) does hold, this inclusion map should be understood through transfer maps between Hochshild cohomology rings of the blocks B and C. We showed that the (B, C) -bimodule L which is the Green correspondent of C to G x H has many nice properties which are useful not only for applications for the cohomology theory but also for modular representation theory of finite groups. Under some additional conditions the module L defines the transfer map L:HH^* (B)→ HH^* (C) which induce the inclusion map l:H^* (G,B)→ H^* (H,C) through embeddings of H^* (G, B) into HH^* (B) and of H^* (H,C) into HH^* (c). It is very interesting from a view point of modular representation theory to determine the blocks of kH in which the Green correspondent V of an indecomposable module U lying in the block B lies. We showed that, using the module L above that under some condition the module V lies in the Brauer correspondent C and when H^* (G,B)⊆ H^* (H,C) the block varieties of the modules coincides in the sense that V _(G,B)(U)= l^* V _(H,C)(V).
-
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
2003.4 - 2006.3
日本学術振興会 科学研究費補助金 若手研究(B)
平野 幹
Authorship：Principal investigator Grant type：Competitive
-
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
2001.4 - 2003.3
日本学術振興会 科学研究費補助金 若手研究(B)
平野 幹
Authorship：Principal investigator Grant type：Competitive
-
Study on automorphic forms on algebraic groups and associated zeta functions
2001 - 2004
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
MURASE Atsushi, SUGANO Takashi, ITO Masami, NARITA Hiroaki, HIRANO Miki, OHNO Yasuo
Grant amount：\12200000 （ Direct Cost: \12200000 ）
1. Metaplectic representations of unitary groups :
We studied metaplectic representations of unitary groups over local fields and gave their "universal" splitting, which are in particular useful in the study of theta lifting. As an application of this result, we gave an explicit character formula for metaplectic representations.
2. Fourier-Jacobi expansion of automorphic form on unitary groups of degree three :
We reformulated Shintani' s theory on Fourier-Jacobi expansion of automorphic forms on unitary groups of degree three in adelic language, and calculated explicit form for Fourier-Jacobi expansion of Eisenstein series and Kudla lifts, theta lifts from elliptic modular forms. As an application, we gave a criterion for the non-vanishing of Kudla lifts.
3. Siegel-Weil formula :
We studied a non-regularized Siegel-Weil formula in the case of the dual reductive pair (U(2,2), U(2, 1)).
4. Inner product formula for Kudla lifts :
Using the formula stated in 3, we gave an explicit formula for the Petersson norms of Kudla lifts in term of special values of automorphic L-functions. As an application, we gave a criterion for the non-vanishing of Kudla lifts different from the one given in 2. (The studies 2- 4 are joint works with Takashi Sugano).
5. Support for the Summer School of Number Theory :
We supported financially the Summer School of Number Theory held annually.
The themes were as follows : "Zeta functions" in 2001, "Prehomogeneous vector spaces" in 2002, "Iwasawa theory" in 2003 and "Fundamental groups and Galois representations" in 2004. -
保型形式・保型表現、および関連するゼータ関数
1999
日本学術振興会 科学研究費助成事業 特別研究員奨励費
平野 幹
Grant amount：\1200000 （ Direct Cost: \1200000 ）
-
Automorphic Forms,Automorphic Representations,and Zeta Functions
Grant type：Competitive
Teaching Experience (On-campus)
Social Activities
-
S.C.M.21定例会における講演
Role(s)： Lecturer
S.C.M.21 2020.9
-
愛媛経済研究会
Role(s)： Lecturer
愛媛経済研究会 2017.10
-
19th Autumn Workshop on Number Theory
Role(s)： Planner, Organizing member
Miki Hirano, Taku Ishii, Tadashi Miyazaki, Hiroki Aoki 2016.11