Nevanlinna Theory And Its Relation To Diophantine Approximation
DOWNLOAD
Download Nevanlinna Theory And Its Relation To Diophantine Approximation PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Nevanlinna Theory And Its Relation To Diophantine Approximation book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Nevanlinna Theory And Its Relation To Diophantine Approximation Second Edition
DOWNLOAD
Author : Min Ru
language : en
Publisher: World Scientific
Release Date : 2021-03-10
Nevanlinna Theory And Its Relation To Diophantine Approximation Second Edition written by Min Ru and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.
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 Theory In Several Complex Variables And Diophantine Approximation
DOWNLOAD
Author : Junjiro Noguchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-09
Nevanlinna Theory In Several Complex Variables And Diophantine Approximation written by Junjiro Noguchi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-09 with Mathematics categories.
The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research. Chapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem for entire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.
Nevanlinna S Theory Of Value Distribution
DOWNLOAD
Author : William Cherry
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-04-24
Nevanlinna S Theory Of Value Distribution written by William Cherry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-24 with Mathematics categories.
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.
Diophantine Approximations And Value Distribution Theory
DOWNLOAD
Author : Paul Alan Vojta
language : en
Publisher: Springer
Release Date : 2006-11-15
Diophantine Approximations And Value Distribution Theory written by Paul Alan Vojta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Nevanlinna Theory And Its Relation To Diophantine Approximation
DOWNLOAD
Author : Min Ru
language : en
Publisher:
Release Date : 2021
Nevanlinna Theory And Its Relation To Diophantine Approximation written by Min Ru and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Diophantine approximation categories.
"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"--Provided by publisher.
Introduction To Complex Hyperbolic Spaces
DOWNLOAD
Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Introduction To Complex Hyperbolic Spaces written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Since the appearance of Kobayashi's book, there have been several re sults at the basic level of hyperbolic spaces, for instance Brody's theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super sede Kobayashi's. My interest in these matters stems from their relations with diophan tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case and made substantial progress, after the line started by Grauert and Grauert-Reckziegel and continued by a recent paper of Riebesehl. The book is divided into three main parts: the basic complex analytic theory, differential geometric aspects, and Nevanlinna theory. Several chapters of this book are logically independent of each other.
Compact Riemann Surfaces And Algebraic Curves
DOWNLOAD
Author : Kichoon Yang
language : en
Publisher: World Scientific
Release Date : 1988
Compact Riemann Surfaces And Algebraic Curves written by Kichoon Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
This volume is an introduction to the theory of Compact Riemann Surfaces and algebraic curves. It gives a concise account of the elementary aspects of different viewpoints in curve theory. Foundational results on divisors and compact Riemann surfaces are also stated and proved.
Research Problems In Function Theory
DOWNLOAD
Author : Walter K. Hayman
language : en
Publisher: Springer Nature
Release Date : 2019-09-07
Research Problems In Function Theory written by Walter K. Hayman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-07 with Mathematics categories.
In 1967 Walter K. Hayman published ‘Research Problems in Function Theory’, a list of 141 problems in seven areas of function theory. In the decades following, this list was extended to include two additional areas of complex analysis, updates on progress in solving existing problems, and over 520 research problems from mathematicians worldwide. It became known as ‘Hayman's List’. This Fiftieth Anniversary Edition contains the complete ‘Hayman's List’ for the first time in book form, along with 31 new problems by leading international mathematicians. This list has directed complex analysis research for the last half-century, and the new edition will help guide future research in the subject. The book contains up-to-date information on each problem, gathered from the international mathematics community, and where possible suggests directions for further investigation. Aimed at both early career and established researchers, this book provides the key problems and results needed to progress in the most important research questions in complex analysis, and documents the developments of the past 50 years.
Nevanlinna S Theory Of Value Distribution
DOWNLOAD
Author : William Cherry
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Nevanlinna S Theory Of Value Distribution written by William Cherry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
On the one hand, this monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution because the authors only assume the reader is familiar with the basics of complex analysis. On the other hand, the monograph also serves as a valuable reference for the research specialist because the 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.
The Legacy Of Niels Henrik Abel
DOWNLOAD
Author : Olav Arnfinn Laudal
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
The Legacy Of Niels Henrik Abel written by Olav Arnfinn Laudal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
This book contains a series of research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields. Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century. It is accompanied by a CD-ROM with a large amount of information related to Niels Henrik Abel, such as on the Abel Centennial in 1902 and the Abel Bicentennial Conference in 2002, the launching of the Abel Prize, Abel monuments, and stamps, banknotes, coins etc. issued in honour of Niels Henrik Abel.