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Introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. Gives applications of the above theory to abc-conjecture, Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Studies interaction theory of rational and entire functions over non- Archimedean fields and Schmidt's subspace theorems, and suggests new problems for further research. The author is affiliated with Shandong University, China.Book News, Inc.®, Portland, OR

Book Description
This book introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. Secondly, it gives applications of the above theory to, e.g., abc-conjecture, Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Next, iteration theory of rational and entire functions over non-Archimedean fields and Schmidt's subspace theorems are studied. Finally, the book suggests some new problems for further research. Audience: This work will be of interest to graduate students working in complex or diophantine approximation as well as to researchers involved in the fields of analysis, complex function theory of one or several variables, and analytic spaces.

Book Info
An introduction to value distribution theory over non-Archimedian fields. Gives applications for the theory and suggests new problems for further research.

FROM THE PUBLISHER

"This book introduces value distribution theory over non-Archimedean fields starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. Secondly, it gives applications of the above theory to, e.g., abc-conjecture. Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Next, iteration theory of rational and entire functions over non-Archimedean fields and Schmidt's subspace theorems are studied. Finally, the book suggests some new problems for further research." "Audience: This work will be of interest to graduate students working in complex or diophantine approximation as well as to researchers involved in the fields of analysis, complex function theory of one or several variables and analytic spaces."--BOOK JACKET.

FROM THE CRITICS

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