Name

NARITA, Hiroaki

Official Title

Professor

Affiliation

(School of Fundamental Science and Engineering)

Sub-affiliation

Sub-affiliation

Faculty of Science and Engineering(Graduate School of Fundamental Science and Engineering)

Affiliated Institutes

理工学術院総合研究所(理工学研究所)

兼任研究員 2018-

Research Grants & Projects

Grant-in-aids for Scientific Research Adoption Situation

Research Classification:

Various constructions of real analytic automorphic forms on real hyperbolic spaces and their application to various research fields

2016/-0-2019/-0

Allocation Class:¥4420000

Research Classification:

Studies on symmetries for automorphic forms and Borcherds products

2014/-0-2017/-0

Allocation Class:¥4680000

Research Classification:

Arithmetic of automorphic forms, an extension of its researching field in terms of explicit constructions

2012/-0-2015/-0

Allocation Class:¥4940000

Research Classification:

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

2011/-0-2014/-0

Allocation Class:¥5070000

Research Classification:

Explicit construction of automorphic forms and its application to number theory and geometry

Allocation Class:¥4160000

Research Classification:

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

Allocation Class:¥4420000

Research Classification:

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

Allocation Class:¥3560000

Research Classification:

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

2019/-0-2022/-0

Allocation Class:¥4030000

On-campus Research System

Special Research Project

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

Research Results Outline: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...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。

実双曲空間上の保型形式の逆定理と周期の研究

2019

Research Results Outline: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...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。

Lecture Course

Course TitleSchoolYearTerm
Perspectives in Mathematical SciencesSchool of Fundamental Science and Engineering2020spring semester
Perspectives in Mathematical Sciences [S Grade]School of Fundamental Science and Engineering2020spring semester
Seminar in Mathematics ASchool of Fundamental Science and Engineering2020spring semester
Seminar in Mathematics A [S Grade]School of Fundamental Science and Engineering2020spring semester
Seminar in Mathematics BSchool of Fundamental Science and Engineering2020fall semester
Seminar in Mathematics B [S Grade]School of Fundamental Science and Engineering2020fall semester
Algebra BSchool of Fundamental Science and Engineering2020full year
Special Exercise on MathematicsSchool of Fundamental Science and Engineering2020fall semester
Supplementary Seminar in Mathematics ASchool of Fundamental Science and Engineering2020spring semester
Supplementary Seminar in Mathematics BSchool of Fundamental Science and Engineering2020fall semester
Undergraduate ResearchSchool of Fundamental Science and Engineering2020full year
Seminar in Applied Mathematics ASchool of Fundamental Science and Engineering2020spring semester
Seminar in Applied Mathematics A [S Grade]School of Fundamental Science and Engineering2020spring semester
Seminar in Applied Mathematics BSchool of Fundamental Science and Engineering2020fall semester
Seminar in Applied Mathematics B [S Grade]School of Fundamental Science and Engineering2020fall semester
Research Project BSchool of Fundamental Science and Engineering2020spring semester
Research Project B [S Grade]School of Fundamental Science and Engineering2020spring semester
Research Project CSchool of Fundamental Science and Engineering2020fall semester
Research Project C [S Grade]School of Fundamental Science and Engineering2020fall semester
Research Project ASchool of Fundamental Science and Engineering2020fall semester
Research Project DSchool of Fundamental Science and Engineering2020spring semester
Advanced Topic in Modern Mathematical Sciences 1School of Fundamental Science and Engineering2020fall quarter
Advanced Topic in Modern Mathematical Sciences 2School of Fundamental Science and Engineering2020winter quarter
Mathematics A1 Sougoukikai(2)School of Creative Science and Engineering2020full year
Master's Thesis (Department of Pure and Applied Mathematics)Graduate School of Fundamental Science and Engineering2020full year
Research on Number Theory and Automorphic FormsGraduate School of Fundamental Science and Engineering2020full year
Research on Number Theory and Automorphic FormsGraduate School of Fundamental Science and Engineering2020full year
Topics in Number Theory CGraduate School of Fundamental Science and Engineering2020spring semester
Topics in Number Theory DGraduate School of Fundamental Science and Engineering2020fall semester
Seminar on Number Theory and Automorphic Forms AGraduate School of Fundamental Science and Engineering2020spring semester
Seminar on Number Theory and Automorphic Forms AGraduate School of Fundamental Science and Engineering2020spring semester
Seminar on Number Theory and Automorphic Forms BGraduate School of Fundamental Science and Engineering2020fall semester
Seminar on Number Theory and Automorphic Forms BGraduate School of Fundamental Science and Engineering2020fall semester
Seminar on Number Theory and Automorphic Forms CGraduate School of Fundamental Science and Engineering2020spring semester
Seminar on Number Theory and Automorphic Forms CGraduate School of Fundamental Science and Engineering2020spring semester
Seminar on Number Theory and Automorphic Forms DGraduate School of Fundamental Science and Engineering2020fall semester
Seminar on Number Theory and Automorphic Forms DGraduate School of Fundamental Science and Engineering2020fall semester
Master's Thesis (Department of Pure and Applied Mathematics)Graduate School of Fundamental Science and Engineering2020full year
Research on Number Theory and Automorphic FormsGraduate School of Fundamental Science and Engineering2020full year