Complementary study on monodromy preserving deformations and new special functions with integral representation

• Project/Area Number: 21740118
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: University of the Ryukyus
• Principal Investigator: MANO Toshiyuki 琉球大学, 理学部, 准教授 (60378594)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: モノドロミ / 積分表示 / 楕円曲線

Research Abstract

We studied properties of the Wirtinger integral which is represented in terms of a definite integral of a power product of theta functions. Moreover, we obtained research results regarding global behaviors of solutions to linear differential equations and detailed properties of monodromy preserving deformations.

Research Products

• [Journal Article] On a generalization of Wirtinger's integral (2012)
  • Author(s): Toshiyuki Mano
  • Journal Title: Kyushu Journal of Mathematics Volume: Vol.66 Pages: 435-447
  • Peer Reviewed
• [Journal Article] Twisted cohomology and homology groups associated to the Riemann-Wirtinger integral (2012)
  • Author(s): Toshiyuki Mano and Humihiko Watanabe
  • Journal Title: Proceedings of the American Mathematical Society Volume: Vol.140 Pages: 3867-3881
  • Peer Reviewed
• [Journal Article] Determinant formula for solutions of the Garnier system and Pade approximation (2012)
  • Author(s): Tohiyuki Mano
  • Journal Title: Journal of Physics A: Mathmatical and Theoretical Volume: Vol.45 Issue: 13 Pages: 135206-135206
  • DOI: 10.1088/1751-8113/45/13/135206
  • Peer Reviewed
• [Journal Article] Monodromy preserving deformation of linear differential equations on a rational nodal curve (2011)
  • Author(s): Tohiyuki Mano
  • Journal Title: Kumamoto Journal of Mathematics Volume: Vol.24 Pages: 1-32
  • NAID: 110009930105
  • Peer Reviewed
• [Journal Article] Monodromy preserving deformation of linear differential equations on arational nodal curve (2011)
  • Author(s): Toshiyuki Mano
  • Journal Title: Kumamoto Journal of Mathematics Volume: 24 Pages: 1-32
  • Peer Reviewed
• [Journal Article] Asymptotic behavior around a boundary point of the q-Painleve VI equation and its connection problem (2010)
  • Author(s): Tohiyuki Mano
  • Journal Title: Nonlinearity Volume: Vol.23 Pages: 1585-1608
  • Peer Reviewed
• [Journal Article] Asymptotic behavior around a boundary point of the q-Painleve VI equation and its connection problem (2010)
  • Author(s): Toshiyuki Mano
  • Journal Title: Nonlinearity Volume: 23 Pages: 1585-1608
  • Peer Reviewed
• [Journal Article] Studies on monodromy preserving deformation of linear differential equations on elliptic curves (2009)
  • Author(s): Toshiyuki Mano
  • Journal Title: Journal of Mathematical Physics Volume: Vol.50 Issue: 10
  • DOI: 10.1063/1.3204973
  • NAID: 120001700241
  • Peer Reviewed
• [Journal Article] Studies on monodromy preserving deformation of linear differential equations on elliptic curves (2009)
  • Author(s): Toshiyuki Mano
  • Journal Title: Journal of Mathematical Physics 50
  • NAID: 120001700241
• [Journal Article] Twisted cohomology and homology groups associated to the Riemann-Wirtinger integral
  • Author(s): Toshiyuki Mano, Humihiko Watanabe
  • Journal Title: Proceedings of the American Mathematical Society Volume: (掲載確定)
  • Peer Reviewed
• [Journal Article] On a generalization of Wirtinger's integral
  • Author(s): Toshiyuki Mano
  • Journal Title: Kyushu Journal of Mathematics Volume: (掲載確定)
  • Peer Reviewed
• [Presentation] Algebraic Painleve VI solutions derived from differential equations on C3 (2013)
  • Author(s): 眞野智行、加藤満生
  • Organizer: 超幾何方程式研究会 2013
  • Place of Presentation: 神戸大学
  • Year and Date: 2013-01-06
• [Presentation] Algebraic Painleve VI solutions derived from free divisors in C3 II (2012)
  • Author(s): 眞 野 智 行
  • Organizer: Workshop on Free Divisors and Differential Equations
  • Place of Presentation: 東京農工大学
  • Year and Date: 2012-11-09
• [Presentation] Algebraic Painleve VI solutoins derived from free divisors in C3 II (2012)
  • Author(s): 眞野智行(代表者)
  • Organizer: Workshop on Free Divisors and Differential Equations
  • Place of Presentation: 東京農工大学
  • Invited
• [Presentation] ガルニエ系の解の行列式公式とパデ近似 (2011)
  • Author(s): 眞野智行
  • Organizer: ガルニエ系の解の行列式公式とパデ近似
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-30
• [Presentation] ガルニエ系の解の行列式公式とパデ近似 (2011)
  • Author(s): 眞野智行
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-30
• [Presentation] モノドロミ保存変形とパデ近似 (2011)
  • Author(s): 眞野智行
  • Organizer: 南九州代数系集会
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2011-08-26
• [Presentation] モノドロミ保存変形とパデ近似 (2011)
  • Author(s): 眞野智行
  • Organizer: 南九州代数細集会
  • Place of Presentation: 鹿児島大学(招待講演)
  • Year and Date: 2011-08-26
• [Presentation] 高階線形微分方程式の合流操作とモノドロミ保存変形の退化 (2010)
  • Author(s): 眞野智行、川向洋之
  • Organizer: Workshop on Accessory Parameters
  • Place of Presentation: 東京大学玉原国際セミナーハウス
  • Year and Date: 2010-10-11
• [Presentation] 高階線形微分方程式の豪州操作とモノドロミ保存変形の退化 (2010)
  • Author(s): 眞野智行、川向洋之
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-24
• [Presentation] 高階線形微分方程式の合流操作とモノドロミ保存変形の退化 (2010)
  • Author(s): 眞野智行、川向洋之
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-24
• [Presentation] 一般 Wirtinger 積分から得られるフックス型方程式のスペクトルデータについて (2010)
  • Author(s): 眞野智行
  • Organizer: アクセサリー・パラメーター研究会
  • Place of Presentation: 熊本大学
  • Year and Date: 2010-03-17
• [Presentation] 一般Wirtinger積分から得られるフックス型方程式のスペクトルデータについて (2010)
  • Author(s): 眞野智行
  • Organizer: アクセサリー・パラメーター研究会
  • Place of Presentation: 熊本大学理学部
  • Year and Date: 2010-03-17
• [Presentation] Riemann-Wirtinger 積分とその応用 (2009)
  • Author(s): 眞野智行
  • Organizer: 微分方程式の総合的研究
  • Place of Presentation: 東京大学
  • Year and Date: 2009-12-18
• [Presentation] Riemann-Wirtinger積分とその応用 (2009)
  • Author(s): 眞野智行
  • Organizer: 研究集会「微分方程式の総合的研究」
  • Place of Presentation: 東京大学数理科学研究科
  • Year and Date: 2009-12-18
• [Presentation] q-PVI 系の境界点における漸近挙動と接続問題 (2009)
  • Author(s): 眞野智行
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-25
• [Presentation] q-PVI系の境界点における漸近挙動と接続問題 (2009)
  • Author(s): 眞野智行
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-25
• [Presentation] he Riemann-Wirtinger integral and its application (2009)
  • Author(s): Toshiyuki Mano
  • Organizer: Third International Conference on Geometry and Quantization GEOQUANT
  • Place of Presentation: University of Luxembourg
  • Year and Date: 2009-09-11
• [Presentation] The Riemann-Wirtinger integral and its application (2009)
  • Author(s): Toshiyuki Mano
  • Organizer: Third International Conference on Geometry and Quantization GEOQUANT
  • Place of Presentation: University of Luxembourg, Luxembourg
  • Year and Date: 2009-09-11