Grant-in-Aid for Scientific Research (B)
|Allocation Type||Single-year Grants |
|Research Institution||KYUSHU UNIVERSITY |
YOSHIDA Masaaki KYUSHU UNIVERSITY, Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (30030787)
SASAKI Takeshi Kobe University, Faculty of Science, Professor, 理学部, 教授 (00022682)
IWASAKI Katsunori KYUSHU UNIVERSITY, Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (00176538)
MIMACHI Katsuhisa Tokyo Inst of Tech., Faculty of Science and engineering, Professor, 大学院・理工学研究科, 教授 (40211594)
MATSUMO Keiji Hokkaido University, Faculty of Science, Associate Professor, 大学院・理学研究科, 助教授 (30229546)
CHO Koji KYUSHU UNIVERSITY, Faculty of Mathematics, Associate Professor, 大学院・数理学研究院, 助教授 (10197634)
花村 昌樹 東北大学, 大学院・理学研究科, 教授 (60189587)
|Project Period (FY)
2002 – 2005
Completed (Fiscal Year 2005)
|Budget Amount *help
¥6,900,000 (Direct Cost: ¥6,900,000)
Fiscal Year 2005: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2004: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2003: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2002: ¥1,800,000 (Direct Cost: ¥1,800,000)
|Keywords||Selberg integral / twisted (co)homology / intersection number / hypergeometric / Whitehead-link / Lambda function / Schwarz triangle / hyperbolic Schwarz map / 捩表裏路地群 / 一寸来群 / 背負ってる回路 / 交叉形式 / 黒写像 / 又曲幾何 / ベタ関数 / 三次曲面 / 又曲構造|
I got the following results concerning the hypergeometric functions.
1)Studied the (co)homology groups attached to Selberg-tpe integrals, evaluated the intersection numbers, and discovered a combinatorial properties of the Selberg functions.
2)Presented co-variant function theory. Found the kappa function, and a 3-parameter families of hypergeometric polynomials, which are very different from the classical ones.
3)Found a new infinite-product formula for the elliptic modular function Lambda.
4)studied combinatorial-topologically the shape of the Schwarz triangles when the inner angles are general.
5)Studied the Whitehead-link-complement group, constructed automorphic functions for this group, and embedded the quotient space to a Euclidean space.
6)Studied the behavior of the solutions of the hypergeometric equation when the exponent-diffences are pure-imaginary, and studied the relation between the space of parameters and the Teichmuler space of genus 2 curves.
7)Invented the theory of hyperbolic Schwarz map. The target of the Schwarz map has been the sphere. Our hypergeometric one has the 3-dimensional hyperbolic space as its target. Group theoretically it is more natural
8)Studied the surfaces on which 3-dimensional Lie group acts, especially ones on which SL(2,R) acts.