Arithmetic and Geometry Around Hypergeometric Functions [electronic resource] : Lecture Notes of a CIMPA Summer School held at Galatasaray University, Istanbul, 2005 / edited by Rolf-Peter Holzapfel, A. Muhammed Uludağ, Masaaki Yoshida.

Hyperbolic Geometry and the Moduli Space of Real Binary Sextics -- Gauss’ Hypergeometric Function -- Moduli of K3 Surfaces and Complex Ball Quotients -- Macbeaths infinite series of Hurwitz groups -- Relative Proportionality on Picard and Hilbert Modular Surfaces -- Hypergeometric Functions and Carlitz Differential Equations over Function Fields -- The Moduli Space of 5 Points on ?1 and K3 Surfaces -- Uniformization by Lauricella Functions — An Overview of the Theory of Deligne-Mostow -- Invariant Functions with Respect to the Whitehead-Link -- On the Construction of Class Fields by Picard Modular Forms -- Algebraic Values of Schwarz Triangle Functions -- GKZ Hypergeometric Structures -- Orbifolds and Their Uniformization -- From the Power Function to the Hypergeometric Function -- Problem Session.

This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.