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Value Distribution Theory Related to Number Theory

2006-10-06 Mathematics
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Release : 2006-10-06
Genre : Mathematics
Kind : eBook
Book Rating : 698/5 ( reviews)

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Book Synopsis Value Distribution Theory Related to Number Theory by : Pei-Chu Hu

Download or read book Value Distribution Theory Related to Number Theory written by Pei-Chu Hu. This book was released on 2006-10-06. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more.

Value Distribution Theory

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 265/5 ( reviews)

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Book Synopsis Value Distribution Theory by : L. Sario

Download or read book Value Distribution Theory written by L. Sario. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Diophantine Approximations and Value Distribution Theory

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 528/5 ( reviews)

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Book Synopsis Diophantine Approximations and Value Distribution Theory by : Paul Alan Vojta

Download or read book Diophantine Approximations and Value Distribution Theory written by Paul Alan Vojta. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt:

Nevanlinna’s Theory of Value Distribution

2001-04-24 Mathematics
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Release : 2001-04-24
Genre : Mathematics
Kind : eBook
Book Rating : 161/5 ( reviews)

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Book Synopsis Nevanlinna’s Theory of Value Distribution by : William Cherry

Download or read book Nevanlinna’s Theory of Value Distribution written by William Cherry. This book was released on 2001-04-24. Available in PDF, EPUB and Kindle. Book excerpt: This monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution as well as a valuable reference for research specialists. Authors present, for the first time in book form, the most modern and refined versions of the Second Main Theorem with precise error terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its number theoretic digressions These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.

Value Distribution Theory

2013-10-03 Mathematics
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Release : 2013-10-03
Genre : Mathematics
Kind : eBook
Book Rating : 176/5 ( reviews)

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Book Synopsis Value Distribution Theory by : Yang Lo

Download or read book Value Distribution Theory written by Yang Lo. This book was released on 2013-10-03. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one excep tion. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 A

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