Nevanlinna Theory In Several Complex Variables And Diophantine Approximation

Author : Junjiro Noguchi
Publisher : Springer Science & Business Media
ISBN 13 : 4431545719
Total Pages : 425 pages
Book Rating : 4.12/5 ( download)

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Download or read book Nevanlinna Theory in Several Complex Variables and Diophantine Approximation written by Junjiro Noguchi and published by Springer Science & Business Media. This book was released on 2013-12-09 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Junjiro Noguchi
Publisher :
ISBN 13 : 9784431545729
Total Pages : 432 pages
Book Rating : 4.27/5 ( download)

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Download or read book Nevanlinna Theory in Several Complex Variables and Diophantine Approximation written by Junjiro Noguchi and published by . This book was released on 2013-12-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Min Ru
Publisher : World Scientific
ISBN 13 : 9811233527
Total Pages : 443 pages
Book Rating : 4.24/5 ( download)

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Download or read book Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition) written by Min Ru and published by World Scientific. This book was released on 2021-03-10 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michael Schneider
Publisher : Cambridge University Press
ISBN 13 : 9780521770866
Total Pages : 582 pages
Book Rating : 4.66/5 ( download)

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Download or read book Several Complex Variables written by Michael Schneider and published by Cambridge University Press. This book was released on 1999 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.

Author : Min Ru
Publisher :
ISBN 13 : 9789811233517
Total Pages : 426 pages
Book Rating : 4.19/5 ( download)

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Download or read book Nevanlinna Theory and Its Relation to Diophantine Approximation written by Min Ru and published by . This book was released on 2021 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Author : Pei-Chu Hu
Publisher : Springer Science & Business Media
ISBN 13 : 3764375698
Total Pages : 546 pages
Book Rating : 4.90/5 ( download)

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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.

Author : Chung-Chun Yang
Publisher : American Mathematical Soc.
ISBN 13 : 0821851640
Total Pages : 188 pages
Book Rating : 4.47/5 ( download)

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Download or read book Several Complex Variables in China written by Chung-Chun Yang and published by American Mathematical Soc.. This book was released on 1993 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today, there is increasing interest in complex geometry, geometric function theory, and integral representation theory of several complex variables. The present collection of survey and research articles comprises a current overview of research in several complex variables in China. Among the topics covered are singular integrals, function spaces, differential operators, and factorization of meromorphic functions in several complex variables via analytic or geometric methods. Some results are reported in English for the first time.

Author : Pietro Corvaja
Publisher : Cambridge University Press
ISBN 13 : 1108424945
Total Pages : 209 pages
Book Rating : 4.43/5 ( download)

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Download or read book Applications of Diophantine Approximation to Integral Points and Transcendence written by Pietro Corvaja and published by Cambridge University Press. This book was released on 2018-05-03 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Diophantine approximation and equations focusing on Schmidt's subspace theorem, with applications to transcendence.

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 1470411016
Total Pages : 339 pages
Book Rating : 4.15/5 ( download)

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Download or read book Advanced Complex Analysis written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2B provides a comprehensive look at a number of subjects of complex analysis not included in Part 2A. Presented in this volume are the theory of conformal metrics (including the Poincaré metric, the Ahlfors-Robinson proof of Picard's theorem, and Bell's proof of the Painlevé smoothness theorem), topics in analytic number theory (including Jacobi's two- and four-square theorems, the Dirichlet prime progression theorem, the prime number theorem, and the Hardy-Littlewood asymptotics for the number of partitions), the theory of Fuschian differential equations, asymptotic methods (including Euler's method, stationary phase, the saddle-point method, and the WKB method), univalent functions (including an introduction to SLE), and Nevanlinna theory. The chapters on Fuschian differential equations and on asymptotic methods can be viewed as a minicourse on the theory of special functions.

Author : Bullett Shaun
Publisher : World Scientific
ISBN 13 : 1786341018
Total Pages : 248 pages
Book Rating : 4.13/5 ( download)

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Download or read book Analysis And Mathematical Physics written by Bullett Shaun and published by World Scientific. This book was released on 2016-12-22 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise reference book on analysis and mathematical physics, leading readers from a foundation to advanced level understanding of the topic. This is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as distributions, Fourier transforms and microlocal analysis, C* Algebras, value distribution of meromorphic functions, noncommutative differential geometry, differential geometry and mathematical physics, mathematical problems of general relativity, and special functions of mathematical physics. Analysis and Mathematical Physics is the sixth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.