Arithmetic study on automorphic forms of several variables
| Project/Area Number |
16K05085
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kindai University |
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Principal Investigator |
Nagaoka Shoyu 近畿大学, 理工学部, 非常勤講師 (20164402)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | modular形式 / 保型形式 / 代数学 / 整数論 |
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| Outline of Final Research Achievements |
I studied on the p-adic propperties of automorphic forms of several variables, especially modular forms of several variables. Strictly seaking, I studied the theta operator, which is a kind of differential operator. I considered the modular form whose image vanishes modulo p. The origin of my study is the discovery that so-called the Igusa cusp form satisfies such property, namely, it becomes a modular form of mod 23 kernel. During the period of study, I clarified what kind of modular form has such property, what kind of modular form with degree n and prime number p becomes an element of mod p kernel of the theta operator.
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| Academic Significance and Societal Importance of the Research Achievements |
modular形式の整数論的性質は，350年間未解決であったフェルマー予想の解決にも用いられた。それは楕円曲線の理論を通して，現代社会に不可欠な暗号理論に応用にされている。報告者の研究対象はは，modular形式を多変数の場合に拡張したもので，前世紀に定義されたものであるが，組織的な研究，とくにその整数論的性質を解明する研究は最近端緒をつけられたものである。報告者の研究は，その多変数modular形式のp進理論というものであるが，最近の研究で，理論物理学との関係も報告され，整数論ばかりでなく，広く社会の他分野へ応用することは，興味深いこれからの研究課題である。
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Report
(5 results)
Research Products
(11 results)
