Download or read book Further Results on Factorization Theory of Meromorphic Functions written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we shall prove some results which, in turn, will allow us to solve some factorization problems in a systematic way. Also, we shall utilize new methods from theory of complex analytic sets and local holomorphic dynamlics to solve some factorization problems. In Chapter 3, by using an extended version of Steinmetz's theorem, we prove that certain class of meromorphic functions is pseudo-prime. Hence, we can prove that under certain conditions, R(z)H(z) is pseudo-prime, where R(z) is a non-constant rational function and H(z) is a finite order periodic function. In Chapter 4, we try to find out all possible factorizations of p(z)H(z) when H is an exponential type periodic function and p is a non-constant polynomial. This confirms a conjecture of G.D. Song and C.C. Yang. In Chapter 5, we shall use results from theory of complex analytic sets to prove certain criteria on the existence of a non-linear entire common right factor of two entire functions. Applying these criteria, we can then prove that if f is an entire function which is pseudo-prime and not of the form H(Q(z)), where H is a periodic entire function and Q is a polynomial, then R(f(z)) is also pseudo-prime for any non-constant rational function R. This result essentially solves a problem of G.D. Song and is a fundamental property of pseudo-prime function. We also give other applications of these criteria to unique factorization problems. In Chapter 6, we consider the unique factorization problems of f o p and p o f where f is a prime transcendental entire function and p is prime polynomal. We shall use methods from local holomorphic dynamics to solve these problems.
Download or read book Fix points And Factorization Of Meromorphic Functions Topics In Complex Analysis written by Chung-chun Yang and published by World Scientific. This book was released on 1990-01-01 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fix-points and factorization of meromorphic functions have become two research topics that have attracted many complex analysts' attention throughout the world; notably in U.S., China, and Japan. The first two chapters reintroduce Nevanlinna's theory of meromorphic functions and Montel's normal families theory for entire functions. Based on these, several theorems on fix-points were derived. The last two chapters introduce the factorization theory and the relationships between the fix-points and factorization; many recent results in factorization theory were reported and related open questions were raised for further study. This book provides a timely introduction to some of the topics that are currently pursued by many complex analysts. For instance, the fix-points of itrates of functions is closely related to the fractal mathematics, which has just been realized to be useful in many branches of engineering and physics as well as in computer graphics.
Download or read book Fix points and Factorization of Meromorphic Functions written by Qitai Zhuang and published by World Scientific. This book was released on 1990 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fix-points and factorization of meromorphic functions have become two research topics that have attracted many complex analysts' attention throughout the world; notably in U.S., China, and Japan. The first two chapters reintroduce Nevanlinna's theory of meromorphic functions and Montel's normal families theory for entire functions. Based on these, several theorems on fix-points were derived. The last two chapters introduce the factorization theory and the relationships between the fix-points and factorization; many recent results in factorization theory were reported and related open questions were raised for further study. This book provides a timely introduction to some of the topics that are currently pursued by many complex analysts. For instance, the fix-points of itrates of functions is closely related to the fractal mathematics, which has just been realized to be useful in many branches of engineering and physics as well as in computer graphics.
Download or read book Factorization Theory of Meromorphic Functions and Related Topics written by Chung-Chun Yang and published by . This book was released on 1982 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Factorization of Meromorphic Functions written by Fred Gross and published by . This book was released on 1973 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Factorization of Meromophic Functions written by United States. Naval Research Office and published by . This book was released on 1972 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex Analysis Kentucky 1976 written by J. D. Buckholtz and published by Springer. This book was released on 2006-11-14 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Meromorphic Functions over Non Archimedean Fields written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nevanlinna theory (or value distribution theory) in complex analysis is so beautiful that one would naturally be interested in determining how such a theory would look in the non Archimedean analysis and Diophantine approximations. There are two "main theorems" and defect relations that occupy a central place in N evanlinna theory. They generate a lot of applications in studying uniqueness of meromorphic functions, global solutions of differential equations, dynamics, and so on. In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications. In value distribution theory, the main problem is that given a holomorphic curve f : C -+ M into a projective variety M of dimension n and a family 01 of hypersurfaces on M, under a proper condition of non-degeneracy on f, find the defect relation. If 01 n is a family of hyperplanes on M = r in general position and if the smallest dimension of linear subspaces containing the image f(C) is k, Cartan conjectured that the bound of defect relation is 2n - k + 1. Generally, if 01 is a family of admissible or normal crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. Here we list the process of this problem: A. Complex analysis: (i) Constant targets: R. Nevanlinna[98] for n = k = 1; H. Cartan [20] for n = k > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman's conjecture partially solved by Hu-Yang [71J; Griffiths-Lang's conjecture (open).
Download or read book On Periodic Left Factors of Meromorphic Functions written by Fred Gross and published by . This book was released on 1969 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Review written by and published by . This book was released on 1982 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Entire Functions and Related Parts of Analysis written by Jacob Korevaar and published by American Mathematical Soc.. This book was released on 1968-12-31 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Value Distribution of L Functions written by Jörn Steuding and published by Springer. This book was released on 2007-05-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.
Download or read book Proceedings Of The Second Asian Mathematical Conference 1995 written by S Tangmanee and published by World Scientific. This book was released on 1998-02-17 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume covers the main fields of mathematics: analysis, algebra and number theory, geometry and topology, combinatorics and graphs, applied mathematics, numerical analysis and computer mathematics, probability and statistics, teaching and popularization of mathematics.
Download or read book NRL Review written by and published by . This book was released on 1980 with total page 956 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hypercomplex Analysis written by Irene Sabadini and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains selected papers from the ISAAC conference 2007 and invited contributions. This book covers various topics that represent the main streams of research in hypercomplex analysis as well as the expository articles. It is suitable for researchers and postgraduate students in various areas of mathematical analysis.
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 Uniqueness Theory of Meromorphic Functions written by Chung-Chun Yang and published by Springer Science & Business Media. This book was released on 2004-10-04 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there is the unique function satisfying given hypotheses. Developed by R. Nevanlinna, a Finnish mathematician, early in the 1920's, research in the field has developed rapidly over the past three decades with a great deal of fruitful results. This book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results. In addition, useful skills and simple proofs are introduced. This book is suitable for higher level and graduate students who have a basic grounding in complex analysis, but will also appeal to researchers in mathematics.
