Author : Vladimir Gennadievich Sprindzhuk
Publisher :
Page : 186 pages
File Size : 17,15 MB
Release : 1979
Category : Mathematics
ISBN :
This monograph is a systematic presentation of a branch of number theory known as the metric theory of Diophantine approximation. The main emphasis is on extremal problems, i.e., problems involving approximations that are best in a certain sense.
Author : Paul Alan Vojta
Publisher : Springer
Page : 141 pages
File Size : 49,2 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540474528
Author : Vladimir Gennadievič Sprindžuk
Publisher :
Page : pages
File Size : 13,30 MB
Release : 1979
Category :
ISBN :
Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 40,25 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461242207
The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere. Each chapter works out a special case of a much broader general theory, as yet unknown. Indications for this are given throughout the book, together with reference to current publications. The book may be used in a course in number theory, whose students will thus be put in contact with interesting but accessible problems on the ground floor of mathematics.
Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 146 pages
File Size : 36,84 MB
Release : 1995-06-29
Category : Mathematics
ISBN : 9780387944562
The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere. Each chapter works out a special case of a much broader general theory, as yet unknown. Indications for this are given throughout the book, together with reference to current publications. The book may be used in a course in number theory, whose students will thus be put in contact with interesting but accessible problems on the ground floor of mathematics.
Author : V. I. Bernik
Publisher : Cambridge University Press
Page : 198 pages
File Size : 46,93 MB
Release : 1999-10-14
Category : Mathematics
ISBN : 9780521432757
This book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. All researchers with an interest in Diophantine approximation will welcome this book.
Author : Wolfgang M. Schmidt
Publisher : Springer
Page : 224 pages
File Size : 37,8 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540473742
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
Author : W.M. Schmidt
Publisher : Springer
Page : 312 pages
File Size : 49,14 MB
Release : 2009-02-05
Category : Mathematics
ISBN : 3540386459
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
Author : Min Ru
Publisher : World Scientific
Page : 443 pages
File Size : 20,7 MB
Release : 2021-03-10
Category : Mathematics
ISBN : 9811233527
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 : Mumtaz Hussain
Publisher :
Page : 0 pages
File Size : 16,46 MB
Release : 2010
Category :
ISBN :
