Hypergeometric Functions, My Love: Modular Interpretations of Configuration Spaces (Aspects of Mathematics, Vol. 32)

This volume concentrates on hypergeometric functions, starting from the elementary level of equivalence relations to the exponential function. Topics covered include: the configuration space of four points on the projective line; elliptic curves; elliptic modular functions and the theta functions; spaces of six points in the projective plain; K3 surfaces; and theta functions in four variables. The classical story - of the hypergeometric functions, the configuration space of 4 points on the projective line, elliptic curves, elliptic modular functions and the theta functions - now evolves, in this book, to the story of hypergeometric funktions in 4 variables, the configuration space of 6 points in the projective plane, K3 surfaces, theta functions in 4 variables. This modern theory has been established by the author and his collaborators in the 1990's; further development to different aspects is expected. It leads the reader to a fascinating 4-dimensional world. The author tells the story casually and visually in a plain language, starting form elementary level such as equivalence relations, the exponential function, ... Undergraduate students should be able to enjoy the text. Masaaki Yoshida. Includes Bibliographical References (p. 277-283) And Index.