Nevanlinna Theory and Its Relation to Diophantine Approximation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nevanlinna Theory and Its Relation to Diophantine Approximation write by Min Ru. This book was released on 2001. Nevanlinna Theory and Its Relation to Diophantine Approximation available in PDF, EPUB and Kindle. It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections. This book provides an introduction to both Nevanlinna theory and Diophantine approximation, with emphasis on the analogy between these two subjects. Each chapter is divided into part A and part B. Part A deals with Nevanlinna theory and part B covers Diophantine approximation. At the end of each chapter, a table is provided to indicate the correspondence of theorems. Contents: Nevanlinna Theory for Meromorphic Functions and Roth's Theorem; Holomorphic Curves into Compact Riemann Surfaces and Theorems of Siegel, Roth, and Faltings; Holomorphic Curves in Pn(C) and Schmidt's Sub-Space Theorem; The Moving Target Problems; Equi-Dimensional Nevanlinna Theory and Vojta's Conjecture; Holomorphic Curves in Abelian Varieties and the Theorem of Faltings; Complex Hyperbolic Manifolds and Lang's Conjecture. Readership: Researchers in complex analysis, number theory and complex geometry.
Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition)
Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition) write by Min Ru. This book was released on 2021-03-10. Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition) available in PDF, EPUB and Kindle. 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
Nevanlinna Theory in Several Complex Variables and Diophantine Approximation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nevanlinna Theory in Several Complex Variables and Diophantine Approximation write by Junjiro Noguchi. This book was released on 2013-12-09. Nevanlinna Theory in Several Complex Variables and Diophantine Approximation available in PDF, EPUB and Kindle. 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.
Diophantine Approximations and Value Distribution Theory
Diophantine Approximations and Value Distribution Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Diophantine Approximations and Value Distribution Theory write by Paul Alan Vojta. This book was released on 2006-11-15. Diophantine Approximations and Value Distribution Theory available in PDF, EPUB and Kindle.
Nevanlinna’s Theory of Value Distribution
Nevanlinna’s Theory of Value Distribution - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nevanlinna’s Theory of Value Distribution write by William Cherry. This book was released on 2001-04-24. Nevanlinna’s Theory of Value Distribution available in PDF, EPUB and Kindle. 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.
