Updated on 2024/05/21

写真a

 
NARITA, Hiroaki
 
Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor
Degree
博士(数理科学)

Research Experience

  • 2018
    -
    Now

    Waseda University   Faculty of Science and Engineering

  • 2008
    -
    2017

    Kumamoto University   Graduate School of Science and Technology

  • 2008
    -
     

    Associate Professor, ,Graduate School of Science and Technology(Science group),Kumamoto University

  • 2006
    -
    2008

    大阪市立大学 数学研究所 COE研究所員

  • 2006
    -
    2008

    COE Researcher, Advanced Mathematical Institute,Osaka City University

  • 2005
    -
    2006

    マックスプランク数学研究所 客員研究員

  • 2005
    -
    2006

    Guest Researcher,Max-Planck-Institute for Mathematics

  • 2002
    -
    2005

    日本学術振興会 特別研究員

▼display all

Education Background

  •  
    -
    2000

    The University of Tokyo  

  •  
    -
    2000

    The University of Tokyo   Graduate School, Division of Mathematical Sciences  

  •  
    -
    1995

    Waseda University   School of Science and Engineering  

  •  
    -
    1995

    Waseda University   Faculty of Science and Engineering  

Research Areas

  • Algebra

Research Interests

  • 保型形式論

  • 整数論

  • automorphic forms

  • Number theory

 

Papers

  • An explicit lifting construction of CAP forms on O(1,5)

    Hiro-aki Narita, Ameya Pitale, Siddhesh Wagh

    International Journal of Number Theory   19 ( 06 ) 1337 - 1378  2023.02

     View Summary

    In this paper, we explicitly construct nontempered cusp forms on the orthogonal group O(1,5) of signature [Formula: see text]. Given a definite quaternion algebra [Formula: see text] over [Formula: see text], the orthogonal group is attached to the indefinite quadratic space of rank 6 with the anisotropic part defined by the reduced norm of [Formula: see text]. Our construction can be viewed as a generalization of the previous work by the first two authors joint with Masanori Muto to the case of any definite quaternion algebras, for which we note that the work just mentioned takes up the case where the discriminant of [Formula: see text] is two. Unlike the previous work the method of the construction is to consider the theta lifting from Maass cusp forms to O(1,5), following the formulation by Borcherds. The cuspidal representations generated by our cusp forms are studied in detail. We determine all local components of the cuspidal representations and show that our cusp forms are CAP forms.

    DOI

  • Jacquet-Langlands-Shimizu correspondence for theta lifts to GSp(2) and its inner forms II: an explicit formula for Bessel periods and the non-vanishing of theta lifts

    Hiro-aki Narita

    Journal of the mathematical society of Japan   73 ( 1 ) 125 - 159  2021  [Refereed]

  • Modular degrees of elliptic curves and some quotients of L-values

    Kousuke Sugimoto, Hiro-aki Narita

    Tokyo Journal of mathematics   43 ( 2 ) 279 - 293  2020  [Refereed]

    Authorship:Last author

  • An explicit construction of non-tempered cusp forms on O(1,8n+1)

    Yingkun Li, Hiro-aki Narita, Ameya Pitale

    Annales math. Quebec   44 ( 2 ) 349 - 384  2020  [Refereed]

    Authorship:Lead author

  • Jacquet-Langlands-Shimizu correspondence for theta lifts to &ITGSp&IT(2) and its inner forms I: An explicit functorial correspondence

    Hiro-aki Narita, Ralf Schmidt

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   69 ( 4 ) 1443 - 1474  2017.10  [Refereed]

     View Summary

    As was first essentially pointed out by Tomoyoshi Ibukiyama, Hecke eigenforms on the indefinite symplectic group GSp(1,1) or the definite symplectic group GSp*(2) over Q right invariant by a (global) maximal open compact subgroup are conjectured to have the same spinor L-functions as those of paramodular new forms of some specified level on the symplectic group GSp(2) (or GSp(4)). This can be viewed as a generalization of the Jacquet-Langlands-Shimizu correspondence to the case of GSp(2) and its inner forms GSp(1,1) and GSp*(2).& para;& para;In this paper we provide evidence of the conjecture on this explicit functorial correspondence with theta lifts: a theta lift from GL(2) x B-x to GSp(1,1) or GSp*(2) and a theta lift from GL(2) x GL(2) (or GO(2,2)) to GSp(2). Here B denotes a definite quaternion algebra over Q. Our explicit functorial correspondence given by these theta lifts are proved to be compatible with archimedean and non-archimedean local Jacquet-Langlands correspondences. Regarding the non-archimedean local theory we need some explicit functorial correspondence for spherical representations of the inner form and non-supercuspidal representations of GSp(2), which is studied in the appendix by Ralf Schmidt.

    DOI

    Scopus

    2
    Citation
    (Scopus)
  • LIFTING TO GL(2) OVER A DIVISION QUATERNION ALGEBRA, AND AN EXPLICIT CONSTRUCTION OF CAP REPRESENTATION

    Masanori Muto, Hiro-Aki Narita, Ameya Pitale

    NAGOYA MATHEMATICAL JOURNAL   222 ( 1 ) 137 - 185  2016.06  [Refereed]

     View Summary

    The aim of this paper is to carry out an explicit construction of CAP representations of GL(2) over a division quaternion algebra with discriminant two. We first construct cusp forms on such a group explicitly by lifting from Maass cusp forms for the congruence subgroup Gamma(0)(2). We show that this lifting is nonzero and Hecke-equivariant. This allows us to determine each local component of a cuspidal representation generated by such a lifting. We then show that our cuspidal representations provide examples of CAP (cuspidal representation associated to a parabolic subgroup) representations, and, in fact, counterexamples to the Ramanujan conjecture.

    DOI

    Scopus

    5
    Citation
    (Scopus)
  • Fourier expansion of Arakawa lifting II: Relation with central L-values

    Atsushi Murase, Hiro-aki Narita

    INTERNATIONAL JOURNAL OF MATHEMATICS   27 ( 1 )  2016.01  [Refereed]

     View Summary

    This is a continuation of our previous paper [Fourier expansion of Arakawa lifting I: An explicit formula and examples of non-vanishing lifts, Israel J. Math. 187 (2012) 317-369]. The aim of the paper here is to study the Fourier coefficients of Arakawa lifts in relation with central values of automorphic L-functions. In the previous paper we provide an explicit formula for the Fourier coefficients in terms of toral integrals of automorphic forms on multiplicative groups of quaternion algebras. In this paper, after studying explicit relations between the toral integrals and the central L-values, we explicitly determine the constant of proportionality relating the square norm of a Fourier coefficient of an Arakawa lift with the central L-value. We can relate the square norm with the central value of some L-function of convolution type attached to the lift and a Hecke character. We also discuss the existence of strictly positive central values of the L-functions in our concern.

    DOI

    Scopus

    4
    Citation
    (Scopus)
  • Bessel Periods of Theta Lifts to GSp(1,1) and Central Values of Some L-Functions of Convolution Type

    Hiro-aki Narita

    AUTOMORPHIC FORMS: RESEARCH IN NUMBER THEORY FROM OMAN   115   179 - 191  2014  [Refereed]

    DOI

    Scopus

    1
    Citation
    (Scopus)
  • IRREDUCIBILITY CRITERIA FOR LOCAL AND GLOBAL REPRESENTATIONS

    Hiro-Aki Narita, Ameya Pitale, Ralf Schmidt

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   141 ( 1 ) 55 - 63  2013.01  [Refereed]

     View Summary

    It is proved that certain types of modular cusp forms generate irreducible automorphic representations of the underlying algebraic group. Analogous Archimedean and non-Archimedean local statements are also given.

    DOI

    Scopus

    12
    Citation
    (Scopus)
  • SOME VECTOR-VALUED SINGULAR AUTOMORPHIC FORMS ON U(2,2) AND THEIR RESTRICTION TO Sp(1,1)

    Atsuo Yamauchi, Hiro-Aki Narita

    INTERNATIONAL JOURNAL OF MATHEMATICS   23 ( 10 )  2012.10  [Refereed]

     View Summary

    In this paper we provide a construction of theta series on the real symplectic group of signature (1, 1) or the 4-dimensional hyperbolic space. We obtain these by considering the restriction of some vector-valued singular theta series on the unitary group of signature (2, 2) to this indefinite symplectic group. Our (vector-valued) theta series are proved to have algebraic Fourier coefficients, and lead to a new explicit construction of automorphic forms generating quaternionic discrete series representations and automorphic functions on the hyperbolic space.

    DOI

    Scopus

    1
    Citation
    (Scopus)
  • Fourier expansion of Arakawa lifting I: An explicit formula and examples of non-vanishing lifts

    Atsushi Murase, Hiroaki Narita

    Israel Journal of Mathematics   187 ( 1 ) 317 - 369  2012.01  [Refereed]

     View Summary

    Given an elliptic cusp form f and an automorphic form f′ on a definite quaternion algebra over ℚ, there is a theta lifting from (f, f′) to an automorphic form L(f, f′) on the quaternion unitary group GSp(1, 1) generating quaternionic discrete series at the Archimedean place. The aim of this paper is to provide an explicit formula for Fourier coefficients of L(f, f′) in terms of periods of f and f′ with respect to a unitary character χ of an imaginary quadratic field. As an application, we show the existence of (f, f′) with L(f, f′) ≠ 0.

    DOI

    Scopus

    6
    Citation
    (Scopus)
  • Theta lifting from elliptic cusp forms to automorphic forms on Sp(1, q)

    Hiro-aki Narita

    MATHEMATISCHE ZEITSCHRIFT   259 ( 3 ) 591 - 615  2008.07  [Refereed]

     View Summary

    Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by "Kudla lifting", i.e. a theta lifting from elliptic modular forms to holomorphic automorphic forms on SU(1,q). We prove that the images of Arakawa's theta lifting belong to the space of bounded automorphic forms generating quaternionic discrete series, which are non-holomorphic forms. In the appendix we provide the construction of Eisenstein series and Poincare series generating such discrete series.

    DOI

    Scopus

    6
    Citation
    (Scopus)
  • Commutation relations of Hecke operators for Arakawa lifting

    Atsushi Murase, Hiro-Aki Narita

    TOHOKU MATHEMATICAL JOURNAL   60 ( 2 ) 227 - 251  2008.06  [Refereed]

     View Summary

    T. Arakawa. in his Unpublished note, constructed and Studied it theta lifting front elliptic cusp forms to automorphic forms on the quaternion unitary group Of Signature (1. q), The second named author proved that such a lifting provides bounded (or cuspidal) automorphic forms generating quaternionic discrete series. In this paper. restricting ourselves to the case of q = 1. we reformulate Arakawa's theta lifting as it theta correspondence in the adelic setting and determine a commutation relation of Hecke operators satisfied by the lifting. As in application, we show that the theta lift of an elliptic Hecke eigenform is also it Hecke eigenform On the quaternion unitary group. We furthermore Study the spinor L-function attached to the theta lift.

    DOI

    Scopus

    6
    Citation
    (Scopus)
  • Fourier-Jacobi expansion of automorphic forms on Sp-(1, q) generating quaternionic discrete series

    Hiro-aki Narita

    JOURNAL OF FUNCTIONAL ANALYSIS   239 ( 2 ) 638 - 682  2006.10  [Refereed]

     View Summary

    The aim of this paper is to develop the notion of the Fourier expansion of automotphic forms on Sp(1, q) generating quaternionic discrete series, which are non-holomorphic forms. There is such an expansion given by Tsuneo Arakawa, assuming the boundedness of the forms and the integrability of the discrete series. We study these automorphic forms without such assumptions. When q > 1 we prove the "Koecher principle" for such automorphic forms, whose validity is known for holomorphic automorphic forms except elliptic modular forms. (c) 2006 Elsevier Inc. All rights reserved.

    DOI

    Scopus

    10
    Citation
    (Scopus)
  • Fourier expansion of holomorphic modular forms on classical lie groups of tube type along the minimal parabolic subgroup

    H Narita

    ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG   74   253 - 279  2004  [Refereed]

     View Summary

    For holomorphic modular forms,on tube domains, there are two types of known Fourier expansions, i.e. the classical Fourier expansion and the Fourier-Jacobi expansion. Either of them is along a maximal parabolic subgroup. In this paper, we discuss Fourier expansion of holomorphic modular forms on tube domains of classical type along the minimal parabolic subgroup. We also relate our Fourier expansion to the two known ones in terms of Fourier coefficients and theta series appearing in these expansions.

    DOI

    Scopus

    1
    Citation
    (Scopus)
  • Fourier expansion of holomorphic Siegel modular forms of genus n along the minimal parabolic subgroup

    NARITA Hiroaki

    Journal of the Mathematical Sciences, the University of Tokyo   10 ( 2 ) 311 - 353  2003  [Refereed]

    CiNii

  • Fourier expansion of holomorphic Siegel modular forms with respect to the minimal parabolic subgroup

    H Narita

    MATHEMATISCHE ZEITSCHRIFT   231 ( 3 ) 557 - 588  1999.07  [Refereed]

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Presentations

  • EXplicit constructions of non-tempered cusp forms on orthogonal groups of low split ranks

    成田 宏秋  [Invited]

    RIMS共同研究(公開型) 保型形式の解析的・数論的研究 

    Presentation date: 2018.01

  • Explicit constructions of non-tempered cusp forms on orthogonal groups of low split ranks

    成田 宏秋  [Invited]

    The third Japanese-German Number Theory Workshop (at MPIM) 

    Presentation date: 2017.11

  • Fourier expansion of Siegel modular forms along the minimal parabolic subgroup

    成田 宏秋  [Invited]

    第19回整数論オータムワークショップ (於 長野県白馬村 白馬ハイマウントホテル) 

    Presentation date: 2016.11

  • Lifting to an inner form of GL(4) and counterexamples of the Ramanujan conjecture

     [Invited]

    Presentation date: 2014.11

  • Lifting from Maass cusp forms for Γ_0(2) to cusp forms on GL(2) over a division quaternion algebra

     [Invited]

    Presentation date: 2014.01

  • Bessel periods of theta lifts to GSp(1,1) and central values of some L-functions of convolution type

     [Invited]

    International conference on automorphic forms and number theory (at Oman) 

    Presentation date: 2012.02

  • Jacquet-Langlands-Shimizu correspondence for two theta lifts to GSp(2) and GSp(1,1)

     [Invited]

    Presentation date: 2012.01

  • Fourier coefficients of Arakawa lifting and central values of some Rankin-Selberg L-functions

    成田 宏秋  [Invited]

    第55回代数学シンポジウム (於 北海道大学) 

    Presentation date: 2010.08

  • 四元数ユニタリー群Sp(1,q)上の実解析的保型形式について

    成田 宏秋  [Invited]

    第53回代数学シンポジウム (於 いわて県民情報交流センター) 

    Presentation date: 2008.08

  • Generalized Whittaker functions on Sp(1,q) for quaternionic discrete series and their application to automorphic forms

    NARITA Hiroaki  [Invited]

    The northern workshop on representation theory of LIe groups and Lie algebras 

    Presentation date: 2007.03

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Research Projects

  • The construction of new research foundation for automorphic forms based on Fourier expansions in non-abelian directions

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2019.04
    -
    2023.03
     

  • 実双曲空間上の実解析保型形式のリフティングによる多様な構成と多方面分野への応用

    科学研究費補助金(基盤研究C)

    Project Year :

    2016
    -
    2018
     

    成田 宏秋

  • Studies on symmetries for automorphic forms and Borcherds products

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2014.04
    -
    2017.03
     

    MURASE Atsushi, NARITA Hiroaki, SUGANO Takashi, Bernhard Heim

     View Summary

    We investigated on a condition for Siegel modular forms on congruence subgroups to have infinite product expansions. We define a notion of “generalized multiplicative symmetries” for a family of automorphic forms on various levels. We furthermore show that a family of automorphic forms with infinite product expansions satisfies generalized multiplicative symmetries. We also considered a similar problem for Jacobi forms and investigated a relation between infinite product expansions and generalized multiplicative symmetries.
    We show that a Siegel modular form of degree 2 of level 1 which is simultaneously anSaito-Kurokawa lift and a Borchers product is a constant multiple of the Igusa modular form.

  • 保型形式の整数論、具体的構成の観点からの研究領域の拡張

    科学研究費補助金(基盤研究C)

    Project Year :

    2012
    -
    2014
     

    成田 宏秋

  • Arithmetic invariants and automorphic L-functions for automorphic forms of several variables

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2011
    -
    2013
     

    MURASE Atsushi, SUGANO Takashi, NARITA Hiroaki, BERNHARD Heim

     View Summary

    We investigated arithmetic properties of Arakawa lifts, which are automorphic forms on the unitary group of degree two for a quaternion algebra over the rational number field constructed via theta lifting. In particular we obtained a formula for the square of the absolute value of a certain average of Fourier coefficients of an Arakawa lift in terms of special values of automorphic L-functions.
    We characterize the holomorphic Borcherds lifts on orthogonal groups of quadratic forms of signature (2, n+2) in terms of the multiplicative symmetries. We also showed that a similar fact holds for Jacobi forms.

  • 保型形式の具体的構成とその数論的及び幾何学的応用

    科学研究費補助金(若手研究B)

    Project Year :

    2009
    -
    2011
     

    成田 宏秋

  • On automorphic forms on algebraic groups: Arithmetic invariants and automorphic L-functions

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2008
    -
    2010
     

    MURASE Atsushi, NARITA Hiroaki, SUGANO Takashi, BERNHARD Heim

     View Summary

    Several invariants are attached to automorphic forms on algebraic groups. These invariants and relationships between them are very useful for studying the internal structure of automorphic forms. In this research, we investigated relationships between these invariants for automorphic forms of special kind called Aarkawa liftings. Using this result, we proposed certain conjectures on relations between invariants attached to automorphic forms on certain groups. We showed that automorphic forms called Borcherds products have strong symmetries (the multiplicative symmetries). We also studied the Borcherds products in detail in the genus two Siegel modular case. In particular, we obtained several results about the weights and characters of Borcherds products.

  • 四元数離散系列表現を生成する保型形式の解析的及び数論的研究

    科学研究費補助金(若手研究B)

    Project Year :

    2006
    -
    2008
     

    成田 宏秋

  • Research on analysis and arithmetic of automorphic forms generating quaternionic discrete series

    Grant-in-Aid for Scientific Research

    Project Year :

    2006
    -
    2008
     

  • 保型形式の整数論、一般化球関数の観点からの研究

    日本学術振興会  科学研究費助成事業

    Project Year :

    2002
    -
    2004
     

    成田 宏秋

     View Summary

    1.符号(1+,q-)のシンプレクティック群Sp(1,q)上の保型形式の研究
    本年度当初は、計画通りこの保型形式に「原始テータ関数の理論」を整備することを目標にし、原始テータ関数の成す空間の次元公式を与えるところまで進んだ。しかし現時点での研究手法では、次の段階である原始テータ関数の空間のメタプレクティック表現の作用による分解を考えることには限界があると感じた。一方で、この保型形式の研究の更なる進展のためには、その具体的構成を考える必要があると感じ始めていた。そこで本年度途中より、昨年度まで研究していたSp(1,q)の上の四元数離散系列を生成する保型形式の研究に戻り、この保型形式の具体的構成を考えた。その結果、昨年度まで研究していたこの保型形式のフーリエ展開の理論を応用することで、楕円保型形式からこのSp(1,q)上の保型形式へのテータリフトによる構成、アイゼンシュタイン級数及びポアンカレ級数による構成を与えることができた。更に後者の2種類の保型形式が、四元数離散系列を生成する保型形式の空間全体を張ることを示すことができた。
    2.保型形式の次元公式への非中心的べき単元の寄与に関する研究
    本年度の目標は、非中心的べき単元の寄与が消えるという予想の証明の際問題となる和と積分の順序交換の問題を解決することであった。これは次元公式の各寄与が一般に絶対収束とは限らないことに起因する。そこでその解決のため、もっと一般の寄与に関し「非特異化」を与える必要があると考え、昨年6月27日から7月17日の間ダラム大学のバーナーホフマン氏を訪ねこの問題に関する研究討議を行った。その結果次元公式に現れる和を「ブリュワ-セル」に関する和に分解し、その各セルの寄与をアイゼンシュタイン級数の定数項で評価することで、非特異化の然るべき定義を探すというアイデアを得た。しかし、この表題の研究については今年度中の解決には至らなかった。

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Misc

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Syllabus

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Sub-affiliation

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Research Institute

  • 2022
    -
    2024

    Waseda Research Institute for Science and Engineering   Concurrent Researcher

Internal Special Research Projects

  • 一般化Ramanujan予想の非緩増加カスプ形式の特徴付けによるアプローチ

    2022  

     View Summary

    今回の研究期間において、オクラホマ大学のAmeya Pitale氏との共同研究により本研究課題に関係して次の研究を行った。fをレベル1の複素上半平面上のMaassカスプ形式とし、φ(f)を符号(1+,(8n+1)-)の直交群へのテータリフトとするとφ(f)のPeterssonノルムによる正規化のsup normが, ある正の整数dに対して, |λ|^d(λはLaplace固有値)によりこの直交群の算術商のみに依存した定数倍を除いて上から評価できるという観察結果を得た。Peter Sarnakが予想しているtrivial boundによるとdが2nまで評価が改善できるようであるがその改善には至らなかった。しかし既存の結果は任意のコンパクト集合に制限したもので我々はその制限なしで結果を得た。

  • 四元数離散系列表現を生成する保型形式のKoecher原理

    2022  

     View Summary

    多変数の正則保形形式で知られているKoecher原理は「多項式増大性が自動的に満たされる」という主張であるが、私は嘗て階数1の四元数ユニタリー群の四元数離散系列表現を生成する非正則保型形式でKoecher原理を証明した。よってこれが一般の四元数離散系列でも成立すると期待すのが自然と考えてきたが、今回の研究で例外型Lie群G_2上の保型形式について、成り立っていない、ないしは成り立っていとしても、現状では証明するのは難しいと考えるに至った。しかし一方, このG_2の保型形式の中でもカスプ形式の場合で, Koecher原理の研究で重要なFourier-Jacobi展開の理論のアイデアをまとめたと考え論文執筆の着手に至った。

  • 実双曲空間上のテータリフトの内積公式とその応用

    2020   Ameya Pitale

     View Summary

    オクラホマ大学のAmeya Pitale氏との共同研究により、以前より研究していた複素上半平面上のMaassカスプ形式からのテータリフトについて、その内積公式を明示的に求める計算を行ってきた。この公式はEuler積表示を持ち、不分岐有限素点の成分は既に一般的に計算されているが分岐有限素点と無限素点の成分は自力で計算する必要がある。今年度の研究で我々のテータ―リフトの内積公式の無限素点の明示形を求めることができた。有限分岐素点の明示形も導出のための基本的な材料が揃った段階で現時点で「時間が十分あればできる」という段階に至っている。

  • 実双曲空間上の保型形式の逆定理と周期の研究

    2019  

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    有理数体上定符号四元数環係数の2次一般線形群上のカスプ形式のリフティングによる構成について、判別式が2の場合で得られていたものを一般の素数判別式の場合に一般化することができた。また非消滅の例も判別式2の場合以外にいくつか更に与えることができた。周期の研究についてはリフティングのWeil表現による定式化を進めそのPetersson内積などの周期に関連する研究を更に進めることで次年度も継続することとした。逆定理のアデール化についても研究したがBruhat細胞分解の観点からの保型性の特徴づけに部分的解決は得られたもののまだ不十分という現時点での結果となった。本研究はOklahoma大学のAmeya Pitale氏との共同研究に基づく。

  • 実双曲空間上の実解析的保型形式のリフティングによる構成

    2018  

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    これまで行ってきた実双曲空間上の保型形式、特にカスプ形式の具体的構成について、既に与えた具体的構成を広い枠組みで捉える一般論の構築に成功した。より詳細には、これまで複素上半平面上の実解析的Maassカスプ形式からのリフティングによる構成を与えてきたが、これは有限素点で「非緩増加」という性質を満たし、所謂Ramanujan予想の反例条件を満たす。このリフティングの定性的側面として「特殊Bessel模型を持つ」というのがある。本研究期間において、一般の直交群上の保型形式が特殊Bessel模型を持ち且つ「Maass関係式」が成り立つ有限素点が存在すれば、そこで非緩増加であるという一般論を与えた。