Download or read book Value Distribution Theory written by L. Sario and published by Springer. This book was released on 2012-12-07 with total page 236 pages. 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.
Download or read book Value Distribution Theory Related to Number Theory written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2006-10-06 with total page 546 pages. 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.
Download or read book Value Distribution Theory and Related Topics written by Grigor A. Barsegian and published by Springer Science & Business Media. This book was released on 2004-05-31 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume consists of a collection of articles on the value distribution theory and its applications, both in one and several variables. The applied parts include problems related to geometric function theory, linear operators of entire functions, differential and functional equations, uniqueness and interpolation. A unique feature of the book is an extensive research program by the first editor on the Gamma-lines approach to analysis. Some aspects in the book consider Diophantine type equations for meromorphic functions, offering new challenges to complex analysis. Audience: Researchers and postgraduate students in complex analysis, differential equations and algebraic geometry would find this book of interest.
Download or read book Value Distribution Theory written by Yang Lo and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 280 pages. 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
Download or read book Nevanlinna s Theory of Value Distribution written by William Cherry and published by Springer Science & Business Media. This book was released on 2001-04-24 with total page 224 pages. 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.
Download or read book Value Distribution Theory and Complex Dynamics written by William Cherry and published by American Mathematical Soc.. This book was released on 2002 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains six detailed papers written by participants of the special session on value distribution theory and complex dynamics held in Hong Kong at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society in December 2000. It demonstrates the strong interconnections between the two fields and introduces recent progress of leading researchers from Asia. In the book, W. Bergweiler discusses proper analytic maps with one critical point andgeneralizes a previous result concerning Leau domains. W. Cherry and J. Wang discuss non-Archimedean analogs of Picard's theorems. P.-C. Hu and C.-C. Yang give a survey of results in non-Archimedean value distribution theory related to unique range sets, the $abc$-conjecture, and Shiffman's conjecture.L. Keen and J. Kotus explore the dynamics of the family of $f \lambda(z)=\lambda\tan(z)$ and show that it has much in common with the dynamics of the familiar quadratic family $f c(z)=z2+c$. R. Oudkerk discusses the interesting phenomenon known as parabolic implosion and, in particular, shows the persistence of Fatou coordinates under perturbation. Finally, M. Taniguchi discusses deformation spaces of entire functions and their combinatorial structure of singularities of the functions. The bookis intended for graduate students and research mathematicians interested in complex dynamics, function theory, and non-Archimedean function theory.
Download or read book Value Distribution Theory for Meromorphic Maps written by Wilhelm Stoll and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Value distribution theory studies the behavior of mermorphic maps. Let f: M - N be a merom orphic map between complex manifolds. A target family CI ~ (Ea1aEA of analytic subsets Ea of N is given where A is a connected. compact complex manifold. The behavior of the inverse 1 family ["'(CI) = (f- {E )laEA is investigated. A substantial theory has been a created by many contributors. Usually the targets Ea stay fixed. However we can consider a finite set IJ of meromorphic maps g : M - A and study the incidence f{z) E Eg(z) for z E M and some g E IJ. Here we investigate this situation: M is a parabolic manifold of dimension m and N = lP n is the n-dimensional projective space. The family of hyperplanes in lP n is the target family parameterized by the dual projective space lP* We obtain a Nevanlinna theory consisting of several n First Main Theorems. Second Main Theorems and Defect Relations and extend recent work by B. Shiffman and by S. Mori. We use the Ahlfors-Weyl theory modified by the curvature method of Cowen and Griffiths. The Introduction consists of two parts. In Part A. we sketch the theory for fixed targets to provide background for those who are familar with complex analysis but are not acquainted with value distribution theory.
Download or read book Value Distribution Theory and Its Applications written by Chung-Chun Yang and published by American Mathematical Soc.. This book was released on 1983 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Value distribution Theory written by Robert O. Kujala and published by . This book was released on 1974 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
Download or read book Value Distribution Theory written by I. Laine and published by Springer. This book was released on 2006-11-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abstract Analytic Number Theory written by John Knopfmacher and published by Courier Dover Publications. This book was released on 1990-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Knopfmacher (1937-99) was a Professor of Mathematics at the University of the Witwatersrand in Johannesburg, South Africa. ...
Download or read book Distribution Theory of Algebraic Numbers written by Pei-Chu Hu and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions • Algebraic numbers • Algebraic geometry • Height functions • The abc-conjecture • Roth's theorem • Subspace theorems • Vojta's conjectures • L-functions.
Download or read book Value Distribution Theory written by Yang Lo and published by Springer. This book was released on 1993-11-09 with total page 269 pages. 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
Download or read book Diophantine Approximations and Value Distribution Theory written by Paul Alan Vojta and published by Springer. This book was released on 2006-11-15 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Distributions written by M.A. Al-Gwaiz and published by CRC Press. This book was released on 1992-04-24 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook for a graduate course in the theory of distributions and related topics, for students of applied mathematics or theoretical physics. Introduces the theory, explicates mathematical structures and the Hilbert-space aspects, and presents applications to typical boundary problems. Annotation
Download or read book Value Distribution Theory written by I. Laine and published by . This book was released on 2014-01-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Theory Arising From Finite Fields written by John Knopfmacher and published by CRC Press. This book was released on 2001-04-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory" offers a discussion of the advances and developments in the field of number theory arising from finite fields. It emphasizes mean-value theorems of multiplicative functions, the theory of additive formulations, and the normal distribution of values from additive functions
