Study on the arithmetic theory of modular forms of several variables

• Project/Area Number: 19540061
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kinki University
• Principal Investigator: NAGAOKA Shoyu Kinki University, 理工学部, 教授 (20164402)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 整数論 / 保型形式 / モジュラー形式 / p進体

Research Abstract

The p-adic theory of modular forms was studied only in the caseof one variable. I tried to generalize the theory to the case of several variables, for example, Siegel modular forms and Hermitian modular forms, and produced fruits. One ofthem can be formulated as the coincidence between the p-adic Eisenstein series and the genus theta series.

Research Products

• [Journal Article] Congruence Properties of Hermitian modular forms (2009)
  • Author(s): T. Kikuta, S. Nagaoka
  • Journal Title: Proceedings of American Mathematical Society 137巻 Pages: 1179-1184
  • Peer Reviewed
• [Journal Article] Congruence properties of Hermitian modular forms (2009)
  • Author(s): S.Nagaoka
  • Journal Title: Proceedings of American Mathematical Society 137 Pages: 1179-1184
  • Peer Reviewed
• [Journal Article] Congruence properties of Hermitian modular forms (2009)
  • Author(s): S. Nagaoka
  • Journal Title: Proceedings of the American Mathematical Society 137 Pages: 1179-1184
  • Peer Reviewed
• [Journal Article] On a corespondence between p-adic Siegel Eisenstein series and genus theta Series (2008)
  • Author(s): T. Kikuta, S. Nagaoka
  • Journal Title: Acta Arithmetica 134巻 Pages: 111-126
  • Peer Reviewed
• [Journal Article] On a correspondence between p-adic Siegel-Eisenstein series and genus theta series (2008)
  • Author(s): S. Nagaoka
  • Journal Title: Acta Arithmetica 134 Pages: 111-126
  • Peer Reviewed
• [Journal Article] On mod p poperties of Siegel modular forms (2007)
  • Author(s): S. Boecherer, S. Nagaoka
  • Journal Title: Mathematische Annalen 338巻 Pages: 421-433
  • Peer Reviewed
• [Journal Article] On mod p properties of Siegel modular forms (2007)
  • Author(s): S.Boecherer
  • Journal Title: Mathematische Annalen 338 Pages: 421-433
  • Peer Reviewed
• [Journal Article] On Siegel modular forms of level p and their properties mod p
  • Author(s): S. Boecherer, S. Nagaoka
  • Journal Title: manuscripta mathematica (に掲載決定)
  • Peer Reviewed
• [Journal Article] Some congruence for Saito-Kurakawa lifts
  • Author(s): Y. Mizuno, S. Nagaoka
  • Journal Title: Abhhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg (に掲載決定)
  • Peer Reviewed
• [Presentation] On Siegel modular forms of level p and their properties mod p (2009)
  • Author(s): 長岡昇勇
  • Organizer: ドイツOberwolfach数学研究所講演会
  • Place of Presentation: ドイツOberwolfach数学研究所
  • Year and Date: 2009-12-18
• [Presentation] On Hermitian modular forms mod p (2009)
  • Author(s): 長岡昇勇
  • Organizer: 日本数学会総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-26
• [Presentation] On modular forms mod p (2008)
  • Author(s): S. Nagaoka
  • Organizer: Oberwolfach Conference
  • Place of Presentation: ドイツ・オバーボルファツハ数学研究所
  • Year and Date: 2008-12-20
• [Presentation] modular形式のある合同について (2008)
  • Author(s): 長岡昇勇
  • Organizer: 日本数学会総合分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-27
• [Presentation] Some p-adic properties of Siegel-Eisenstein series (2008)
  • Author(s): 長岡 昇勇
  • Organizer: 京都大学数理解析研究所研究集会「保型表現・保型形式とL関数の周辺」
  • Place of Presentation: 京都市京都大学数理解析研究所
  • Year and Date: 2008-01-25
• [Remarks]
  • URL: http://www.math.kindai.ac.jp/~nagaoka