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Arithmetic and Geometry Around Hypergeometric Functions

Lecture Notes of a CIMPA Summer School held at Galatasaray University, Istanbul, 2005

  • Book
  • © 2007

Overview

Editors:
  1. Rolf-Peter Holzapfel

    1. Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin

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  2. A. Muhammed Uludağ

    1. Department of Mathematics, Galatasaray University, Besiktas, Istanbul, Turkey

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    You can also search for this editor in PubMed   Google Scholar

  3. Masaaki Yoshida

    1. Department of Mathematics, Kyushu University, Fukuoka, Japan

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  • Presents reviewed and polished lecture notes, survey articles and original research results written by acknowledged experts in the field
  • Contains a stimulating collection of open problems

Part of the book series: Progress in Mathematics (PM, volume 260)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Hyperbolic Geometry and the Moduli Space of Real Binary Sextics

    • Daniel Allcock, James A. Carlson, Domingo Toledo
    Pages 1-22

  3. Gauss’ Hypergeometric Function

    • Frits Beukers
    Pages 23-42

  4. Moduli of K3 Surfaces and Complex Ball Quotients

    • Igor V. Dolgachev, Shigeyuki Kondō
    Pages 43-100

  5. Macbeaths infinite series of Hurwitz groups

    • Amir Džambić
    Pages 101-108

  6. Relative Proportionality on Picard and Hilbert Modular Surfaces

    • Rolf-Peter Holzapfel
    Pages 109-162

  7. Hypergeometric Functions and Carlitz Differential Equations over Function Fields

    • Anatoly N. Kochubei
    Pages 163-187

  8. The Moduli Space of 5 Points on ℙ1 and K3 Surfaces

    • Shigeyuki Kondō
    Pages 189-206

  9. Uniformization by Lauricella Functions — An Overview of the Theory of Deligne-Mostow

    • Eduard Looijenga
    Pages 207-244

  10. Invariant Functions with Respect to the Whitehead-Link

    • Keiji Matsumoto
    Pages 245-271

  11. On the Construction of Class Fields by Picard Modular Forms

    • Thorsten Riedel
    Pages 273-285

  12. Algebraic Values of Schwarz Triangle Functions

    • Hironori Shiga, Jürgen Wolfart
    Pages 287-312

  13. GKZ Hypergeometric Structures

    • Jan Stienstra
    Pages 313-371

  14. Orbifolds and Their Uniformization

    • A. Muhammed Uludağ
    Pages 373-406

  15. From the Power Function to the Hypergeometric Function

    • Masaaki Yoshida
    Pages 407-429

  16. Problem Session

    • Celal Cem Sarıoğlu
    Pages 431-437
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Keywords

About this book

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.

Editors and Affiliations

  • Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin

    Rolf-Peter Holzapfel

  • Department of Mathematics, Galatasaray University, Besiktas, Istanbul, Turkey

    A. Muhammed Uludağ

  • Department of Mathematics, Kyushu University, Fukuoka, Japan

    Masaaki Yoshida

Bibliographic Information

  • Book Title: Arithmetic and Geometry Around Hypergeometric Functions

  • Book Subtitle: Lecture Notes of a CIMPA Summer School held at Galatasaray University, Istanbul, 2005

  • Editors: Rolf-Peter Holzapfel, A. Muhammed Uludağ, Masaaki Yoshida

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-7643-8284-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkhäuser Basel 2007

  • Hardcover ISBN: 978-3-7643-8283-4Published: 22 January 2007

  • eBook ISBN: 978-3-7643-8284-1Published: 28 June 2007

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: VIII, 437

  • Topics: Special Functions, Algebraic Geometry

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