Studies on automorphic forms and algebraic combinatorics connected via theta map

• Project/Area Number: 21740021
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Kochi University
• Principal Investigator: OURA Manabu 高知大学, 教育研究部自然科学系, 准教授 (50343380)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 代数的組合せ論 / 保型形式 / モジュラー形式 / E-多項式 / 不変式 / Eisenstein級数 / 不変式論 / 符号 / 次数付き環 / 格子

Research Abstract

An E-polynomial is mapped to a modular form. We observed the obtained modular forms in genus 1. Originally E-polynomials are introduced as a counterpart of Eisenstein series and we found similar properties as Eisenstein series. The obtained modular forms have zeros on the circle of radius 1 in the fundamental region and those zeros have the so-called separation property. However, they are not proved and are expected to be clear in our subsequent research.

Research Products

• [Presentation] Modular forms of weight 8 for the theta group (2012)
  • Author(s): 大浦 学
  • Organizer: 第29回代数的組合せ論シンポジウム
  • Place of Presentation: 弘前大学
  • Year and Date: 2012-06-18
• [Presentation] 代数的組合せ論とジーゲルモジュラー形式 (2012)
  • Author(s): 大浦 学
  • Organizer: 保型形式ミニ研究集会
  • Place of Presentation: 近畿大学
  • Year and Date: 2012-03-03
• [Presentation] モジュラー形式としての E-多項式 (2012)
  • Author(s): 大浦 学
  • Organizer: 組合せ論セミナー
  • Place of Presentation: 大分工業高等専門学校
  • Year and Date: 2012-03-01
• [Presentation] Some consequences of the work of Nebe-Rains-Sloane (2011)
  • Author(s): 大浦 学
  • Organizer: Workshop "Lattices, codes and modular forms"
  • Place of Presentation: アアヘン工科大学、ドイツ
  • Year and Date: 2011-09-28
• [Presentation] Some consequences of the work of Nebe-Rains-Sloane (2011)
  • Author(s): 大浦学
  • Organizer: Workshop "Lattices, codes and modular forms"
  • Place of Presentation: Aachen(ドイツ)
  • Year and Date: 2011-09-28
• [Presentation] Some computations concerning to the average weight enumerators (2011)
  • Author(s): 大浦 学
  • Organizer: Japan-Korea workshop on algebraiccombinatorics
  • Place of Presentation: 東北大学
  • Year and Date: 2011-01-24
• [Presentation] Remark on the invariant ringsof finite unitary reflection groups (2010)
  • Author(s): 大浦 学
  • Organizer: Workshop on Algebraic combinatorics
  • Place of Presentation: 河北師範大学、中国
  • Year and Date: 2010-11-26
• [Presentation] Remark on the invariant rings of finite unitary reflection groups (2010)
  • Author(s): 大浦学
  • Organizer: Workshop on Algebraic Combinatorics
  • Place of Presentation: 河北師範大学(中国)
  • Year and Date: 2010-11-26
• [Remarks]
  • URL: http://www.math.kochi-u.ac.jp/oura
• [Remarks]
  • URL: http://www.math.kochi-u.ac.jp/oura/index.html
• [Remarks]
  • URL: http://www.math.kochi-u.ac.jp/oura