Download or read book Diophantine Approximation and Abelian Varieties written by Bas Edixhoven and published by Springer. This book was released on 2009-02-05 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Diophantine Approximation and Abelian Varieties written by and published by . This book was released on 1993 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Diophantine Approximation and Abelian Varieties written by Bas Edixhoven and published by . This book was released on 2014-01-15 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Diophantine Geometry written by Marc Hindry and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Download or read book On Some Applications of Diophantine Approximations written by Umberto Zannier and published by Springer. This book was released on 2015-02-13 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper "Über einige Anwendungen diophantischer Approximationen" by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel’s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel’s paper. To end, it presents three modern proofs of Siegel’s theorem on integral points.

Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2015-12-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.

Download or read book O Minimality and Diophantine Geometry written by G. O. Jones and published by Cambridge University Press. This book was released on 2015-08-13 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the researcher up to date with recent applications of mathematical logic to number theory.

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1993-01-31 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Download or read book Diophantine Approximation and Abelian Varieties written by Bas Edixhoven and published by Springer. This book was released on 1993 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book Diophantine Approximation written by David Masser and published by Springer. This book was released on 2008-02-01 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine Approximation is a branch of Number Theory having its origins intheproblemofproducing“best”rationalapproximationstogivenrealn- bers. Since the early work of Lagrange on Pell’s equation and the pioneering work of Thue on the rational approximations to algebraic numbers of degree ? 3, it has been clear how, in addition to its own speci?c importance and - terest, the theory can have fundamental applications to classical diophantine problems in Number Theory. During the whole 20th century, until very recent times, this fruitful interplay went much further, also involving Transcend- tal Number Theory and leading to the solution of several central conjectures on diophantine equations and class number, and to other important achie- ments. These developments naturally raised further intensive research, so at the moment the subject is a most lively one. This motivated our proposal for a C. I. M. E. session, with the aim to make it available to a public wider than specialists an overview of the subject, with special emphasis on modern advances and techniques. Our project was kindly supported by the C. I. M. E. Committee and met with the interest of a largenumberofapplicants;forty-twoparticipantsfromseveralcountries,both graduatestudentsandseniormathematicians,intensivelyfollowedcoursesand seminars in a friendly and co-operative atmosphere. The main part of the session was arranged in four six-hours courses by Professors D. Masser (Basel), H. P. Schlickewei (Marburg), W. M. Schmidt (Boulder) and M. Waldschmidt (Paris VI). This volume contains expanded notes by the authors of the four courses, together with a paper by Professor Yu. V.

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 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Degeneration of Abelian Varieties written by Gerd Faltings and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.

Download or read book Diophantine Approximations and Value Distribution Theory written by Paul Alan Vojta and published by Springer. This book was released on 2006-11-15 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modular Curves and Abelian Varieties written by John Cremona and published by Birkhäuser. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matemtica (Bellaterra, Barcelona). The articles in this volume present the latest achievements in this extremely active field and will be of interest both to specialists and to students and researchers. Many contributions focus on generalizations of the Shimura-Taniyama conjecture to varieties such as elliptic Q-curves and Abelian varieties of GL_2-type. The book also includes several key articles in the subject that do not correspond to conference lectures.

Download or read book Abelian Varieties with Complex Multiplication and Modular Functions written by Goro Shimura and published by Princeton University Press. This book was released on 2016-06-02 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively.