The recent advancements，new results and applications of complex analysis and p-adic analysis are rather extensive．In this book，the focus centers on those topics which pertain to two intrinsic properties of analytic functions：value distribution and complex differentiability．Complex analysis and p-adic analysis are two closely linked，old branches of mathematics that have played a prominent role in the development of modem mathematics．

Preface

List of Contributors

Part Ⅰ Value Distribution of Complex and P-adic Functions

Chapter 1 The Second Main Theorem on Generalized Parabolic Manifolds

 1.1 Monge-Ampere equations and generalized parabolic manifolds

 1.2 Projectivized bundles over Stein manifolds

 1.3 Meromorphic global forms

 1.4 Analytic and algebraic Pliicker Formulas: The classical case

 1.5 Plucker's formulas for generalized parabolic manifolds

 1.6 An analogue of the Ahlfors-Stoll estimate

 1.7 The second main theorem

Chapter 2 P-adic Value Distribution

 2.1 Ultrametric analytic functions

 2.2 Lazard's problem and p-adic Nevanlinna theory

 2.3 Applications of the Nevanlinna theory

Chapter 3 Survey on Meromorphic Functions of Uniqueness

 3.1 Introduction and basic results

 3.2 Main results and examples

Chapter 4 A Survey on Uniqueness Polynomials and Unique Range Sets

 4.1 Meromorphic functions sharing points

 4.2 Unique range set for meromorphic functions

 4.3 Uniqueness polynomials for meromorphic functions

Chapter 5 On Petrenko's Theory of Growth of Meromorphic Functions

 5.1 The growth of functions meromorphic in the plane

 5.2 The growth of functions meromorphic in the disc

 5.3 Separated maximum modulus points of entire and meromorphic functions

 5.4 Strong asymptotic values and strong asymptotic spots of entire and meromorphic functions

Chapter 6 Linear Operators, Fourier Transforms and the Riemann ξ-function

 6.1 The Laguerre-P61ya class and the Riemann ξ-function

 6.2 Complex zero decreasing sequences and λ-sequences

 6.3 The distribution of zeros of Fourier transforms

 6.4 Infinite order differential operators and the Riemann ξ-function

Chapter 7 Hyperbolic Hypersurfaces of Lower Degrees

 7.1 Introduction and main techniques

 7.2 Hyperbolic curves

 7.3 Hyperbolic surfaces

 7.4 Hyperbolic hypersurfaces in P4(C)

Chapter 8 Admissible Solutions of Functional Equations of Diophantine Type

 8.1 Introduction

 8.2 Background and results

 8.3 Preliminary lemmas

 8.4 Proofs of the results

Part Ⅱ New Applications of the Concept of Differentiability

Part Ⅲ Boundary Value Problems