Value Distribution Theory

1. Front Matter

   Pages i-4

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2. Introduction

   • Leo Sario, Kiyoshi Noshiro

   Pages 5-10

3. Mappings into Closed Riemann Surfaces

   • Leo Sario, Kiyoshi Noshiro

   Pages 11-41

4. Mappings into Open Riemann Surfaces

   • Leo Sario, Kiyoshi Noshiro

   Pages 42-73

5. Functions of Bounded Characteristic

   • Leo Sario, Kiyoshi Noshiro

   Pages 74-97

6. Functions on Parabolic Riemann Surfaces

   • Leo Sario, Kiyoshi Noshiro

   Pages 98-119

7. Picard Sets

   • Leo Sario, Kiyoshi Noshiro

   Pages 120-135

8. Riemannian Images

   • Leo Sario, Kiyoshi Noshiro

   Pages 136-178

9. Back Matter

   Pages 179-236

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The purpose of this research monograph is to build up a modern value distribution theory for complex analytic mappings between abstract Riemann surfaces. All results presented herein are new in that, apart from the classical background material in the last chapter, there is no over­ lapping with any existing monograph on merom orphic functions. Broadly speaking the division of the book is as follows: The Introduction and Chapters I to III deal mainly with the theory of mappings of arbitrary Riemann surfaces as developed by the first named author; Chapter IV, due to Nakai, is devoted to meromorphic functions on parabolic surfaces; Chapter V contains Matsumoto's results on Picard sets; Chapter VI, pre­ dominantly due to the second named author, presents the so-called nonintegrated forms of the main theorems and includes some joint work by both authors. For a complete list of writers whose results have been discussed we refer to the Author Index.

• Finite
• Meromorphic function
• Riemann surface
• distribution
• equation
• extrema
• function
• integral
• integral equation
• minimum
• proof
• theorem

• University of California, Los Angeles, USA

  Leo Sario

• Nagoya University, Nagoya, Japan

  Kiyoshi Noshiro

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