HIRANO Miki

J-GLOBAL         Last updated: Mar 22, 2019 at 18:10
 
Avatar
Name
HIRANO Miki
Affiliation
Ehime University
Section
Graduate School of Science and Engineering, Mathematics, Physics, and Earth Sciences, Graduate School of Science and Engineering Mathematics,Physics, and Earth Sciences
Job title
Professor,Departmental Dean

Research Areas

 
 

Education

 
 
 - 
1998
Graduate School, Division of Mathematical Sciences, The University of Tokyo
 
 
 - 
1993
Faculty of Science and Engineering, Keio University
 

Published Papers

 
Miki Hirano, Taku Ishii, Tadashi Miyazaki
Proceedings of the Japan Academy Series A: Mathematical Sciences   92 27-32   Jan 2016
© 2016 The Japan Academy. We consider here the archimedean zeta integrals for GL(3) × GL(2) and show that the zeta integral for appropriate Whittaker functions is equal to the associated L-factor.
HIRANO Miki, KATATA Kohei, YAMASAKI Yoshinori
Bulletin of the Australlian Mathematical Society   94(3) 373-383   Dec 2016   [Refereed]
The Archimedean Whittaker functions on GL(3)
HIRANO Miki, ISHII Taku, MIYAZAKI Tadashi
Geometry and analysis of automorphic forms of several variables   77-109   2012   [Refereed]
Jackson q-Mahler measures
HIRANO Miki, KUROKAWA Nobushige
Funct. Approx. Comment. Math   42(1) 51-58   2010   [Refereed]
Miki Hirano, Takayuki Oda
Journal of Functional Analysis   256 2222-2267   Apr 2009
In this paper, we discuss the Whittaker functions for the non-spherical principal series representations of GL (3, C). In particular, we give explicit formulas for these functions. © 2008 Elsevier Inc. All rights reserved.
Miki Hirano, Taku Ishii, Takayuki Oda
Advances in Mathematics   215 734-765   Nov 2007
In this paper, we give explicit formulas for the secondary and the primary Whittaker functions for PJ-principal series representations of Sp (3, R). © 2007 Elsevier Inc. All rights reserved.
Miki Hirano, Taku Ishii, Takayuki Oda
Mathematical Proceedings of the Cambridge Philosophical Society   141 15-31   Jul 2006
We discuss a confluence from Siegel-Whittaker functions to Whittaker functions on Sp(2, ℝ) by using their explicit formulae. In our proof, we use expansion theorems of the good Whittaker functions by the secondary Whittaker functions. © 2006 Cambr...
Miki Hirano, Takayuki Oda
Proceedings of the Japan Academy Series A: Mathematical Sciences   81 105-109   Jun 2005
In this paper, we give explicit formulas for the secondary Whittaker functions for P J-principal series representations of Sp(3, R), which are power series solutions of a holonomic system of rank 24.
Miki Hirano
Indagationes Mathematicae   15 43-54   Jan 2004
In this paper, we study the Fourier-Jacobi type spherical functions on Sp (2, R) for irreducible principal series representations. We give the multiplicity theorem and an explicit formula for this function.
Half zeta functions
HIRANO Miki, KUROKAWA Nobushige, WAKAYAMA Masato
J. Ramanujan Math. Soc.   18(2) 195-209   2003   [Refereed]
Miki Hirano
Journal of the London Mathematical Society   65 524-546   Nov 2002
The paper studies a generalized spherical function, or a generalized Whittaker model for generalized principal series representations of G = Sp(2, R) induced from the Jacobi maximal parabolic subgroup PJ, which is called the Fourier-Jacobi type. I...
Miki Hirano
Transactions of the American Mathematical Society   353(4) 1535-1550   Dec 2001
In this paper, in analogy to the real case, we give a formulation of the Shintani functions on GL(2, C), which have been studied by Murase and Sugano within the theory of automorphic L-functions. Also, we obtain the multiplicity one theorem for th...
Miki Hirano
Compositio Mathematica   128 177-216   Dec 2001
In this paper we define a kind of generalized spherical functions on Sp(2, ℝ). We call it 'Fourier-Jacobi type', since it can be considered as a generalized Whittaker model associated with the Jacobi maximal parabolic subgroup. Also we give the mu...
Shintani functions on GL(2, R)
Transactions of the American Mathematical Society   352(4) 1709-1721   2000
On theta type functions associated with the zeros of the Selberg zeta functions
Manuscripta Mathematica   92(1) 87-105   1997
On Cartier-Voros type Selberg trace formula for congruence subgroups of PSL (2, R)
Proceedings of Japan Academy   71A(7) 144-147   1995
Archimedean zeta integrals for GL(3) × GL(2)
Miki Hirano, Taku Ishii, Tadashi Miyazaki
Memoirs of the American Mathematical Society   to appear    2019   [Refereed]

Conference Activities & Talks

 
Remarks on Ramanujan circulants and dihedrants
HIRANO Miki
26 May 2018   
Ramanujan Cayley graphs and the conjecture of Hardy-Littlewood and Bateman-Horn
HIRANO Miki
2 Dec 2017   
Fourier-Jacobi models on Sp_2(R)
HIRANO Miki
19th Autumn Workshop on Number Theory   5 Nov 2016   

Research Grants & Projects

 
Automorphic Forms,Automorphic Representations,and Zeta Functions

Social Contribution

 
19th Autumn Workshop on Number Theory
[Planner, Organizing Member]  Miki Hirano, Taku Ishii, Tadashi Miyazaki, Hiroki Aoki  2 Nov 2016 - 6 Nov 2016