Value Distribution Theory and Complex Dynamics

Value Distribution Theory and Complex Dynamics
Author :
Publisher : American Mathematical Soc.
Total Pages : 146
Release :
ISBN-10 : 9780821829806
ISBN-13 : 0821829807
Rating : 4/5 (06 Downloads)

Synopsis Value Distribution Theory and Complex Dynamics by : William Cherry

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.

Diophantine Approximation

Diophantine Approximation
Author :
Publisher : Springer Science & Business Media
Total Pages : 416
Release :
ISBN-10 : 9783211742808
ISBN-13 : 3211742808
Rating : 4/5 (08 Downloads)

Synopsis Diophantine Approximation by : Robert F. Tichy

This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation, which are based on lectures given at a conference at the Erwin Schrödinger-Institute (Vienna, 2003). The articles are either in the spirit of more classical diophantine analysis or of a geometric or combinatorial flavor. Several articles deal with estimates for the number of solutions of diophantine equations as well as with congruences and polynomials.

Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition)

Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition)
Author :
Publisher : World Scientific
Total Pages : 443
Release :
ISBN-10 : 9789811233524
ISBN-13 : 9811233527
Rating : 4/5 (24 Downloads)

Synopsis Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition) by : Min Ru

This book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas: one in complex analysis and one in number theory, it has been discovered that a number of striking similarities exist between these two subjects. A growing understanding of these connections has led to significant advances in both fields. Outstanding conjectures from decades ago are being solved.Over the past 20 years since the first edition appeared, there have been many new and significant developments. The new edition greatly expands the materials. In addition, three new chapters were added. In particular, the theory of algebraic curves, as well as the algebraic hyperbolicity, which provided the motivation for the Nevanlinna theory.

Nevanlinna’s Theory of Value Distribution

Nevanlinna’s Theory of Value Distribution
Author :
Publisher : Springer Science & Business Media
Total Pages : 224
Release :
ISBN-10 : 3540664165
ISBN-13 : 9783540664161
Rating : 4/5 (65 Downloads)

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

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 Related to Number Theory

Value Distribution Theory Related to Number Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 546
Release :
ISBN-10 : 9783764375690
ISBN-13 : 3764375698
Rating : 4/5 (90 Downloads)

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

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.

Diophantine Approximation and Abelian Varieties

Diophantine Approximation and Abelian Varieties
Author :
Publisher : Springer Science & Business Media
Total Pages : 136
Release :
ISBN-10 : 9783540575283
ISBN-13 : 3540575286
Rating : 4/5 (83 Downloads)

Synopsis Diophantine Approximation and Abelian Varieties by : Bas Edixhoven

The 13 chapters of this book centre around the proof of Theorem 1 of Faltings' paper "Diophantine approximation on abelian varieties", Ann. Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and algebraic geometry. Each chapter is based on an instructional lecture given by its author ata special conference for graduate students, on the topic of Faltings' paper.

Approximations Diophantiennes et Nombres Transcendants. Diophantine Approximations and Transcendental Numbers

Approximations Diophantiennes et Nombres Transcendants. Diophantine Approximations and Transcendental Numbers
Author :
Publisher : Walter de Gruyter
Total Pages : 321
Release :
ISBN-10 : 9783110861440
ISBN-13 : 3110861445
Rating : 4/5 (40 Downloads)

Synopsis Approximations Diophantiennes et Nombres Transcendants. Diophantine Approximations and Transcendental Numbers by : Patrice Philippon

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Applications of Diophantine Approximation to Integral Points and Transcendence

Applications of Diophantine Approximation to Integral Points and Transcendence
Author :
Publisher : Cambridge University Press
Total Pages : 210
Release :
ISBN-10 : 9781108656566
ISBN-13 : 1108656560
Rating : 4/5 (66 Downloads)

Synopsis Applications of Diophantine Approximation to Integral Points and Transcendence by : Pietro Corvaja

This introduction to the theory of Diophantine approximation pays special regard to Schmidt's subspace theorem and to its applications to Diophantine equations and related topics. The geometric viewpoint on Diophantine equations has been adopted throughout the book. It includes a number of results, some published here for the first time in book form, and some new, as well as classical material presented in an accessible way. Graduate students and experts alike will find the book's broad approach useful for their work, and will discover new techniques and open questions to guide their research. It contains concrete examples and many exercises (ranging from the relatively simple to the much more complex), making it ideal for self-study and enabling readers to quickly grasp the essential concepts.

The Dynamical Mordell–Lang Conjecture

The Dynamical Mordell–Lang Conjecture
Author :
Publisher : American Mathematical Soc.
Total Pages : 297
Release :
ISBN-10 : 9781470424084
ISBN-13 : 1470424088
Rating : 4/5 (84 Downloads)

Synopsis The Dynamical Mordell–Lang Conjecture by : Jason P. Bell

The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point x under the action of an endomorphism f of a quasiprojective complex variety X. More precisely, it claims that for any point x in X and any subvariety V of X, the set of indices n such that the n-th iterate of x under f lies in V is a finite union of arithmetic progressions. In this book the authors present all known results about the Dynamical Mordell-Lang Conjecture, focusing mainly on a p-adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.