Author : Yann Bugeaud
Publisher : Cambridge University Press
Page : 317 pages
File Size : 30,80 MB
Release : 2012-07-05
Category : Mathematics
ISBN : 0521111692
A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, much of it from the last decade. There are numerous exercises to aid student understanding of the topic, and researchers will appreciate the notes at the end of each chapter, extensive references and open problems.
Author : A.N. Parshin
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 11,10 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 3662036444
This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.
Author : Michel Waldschmidt
Publisher : Springer Science & Business Media
Page : 649 pages
File Size : 25,89 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 3662115697
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.
Author : Alan Baker
Publisher : Cambridge University Press
Page : 180 pages
File Size : 42,7 MB
Release : 1990-09-28
Category : Mathematics
ISBN : 9780521397919
First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.
Author : Gregory Chudnovsky
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 49,8 MB
Release : 1984
Category : Mathematics
ISBN : 0821815008
Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.
Author : Yann Bugeaud
Publisher : Cambridge University Press
Page : 292 pages
File Size : 15,66 MB
Release : 2004-11-08
Category : Mathematics
ISBN : 1139455672
An accessible and broad account of the approximation and classification of real numbers suited for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the comprehensive list of more than 600 references.
Author : A. O. Gelfond
Publisher : Courier Dover Publications
Page : 212 pages
File Size : 36,4 MB
Release : 2015-01-05
Category : Mathematics
ISBN : 0486802256
Primarily an advanced study of the modern theory of transcendental and algebraic numbers, this treatment by a distinguished Soviet mathematician focuses on the theory's fundamental methods. The text also chronicles the historical development of the theory's methods and explores the connections with other problems in number theory. The problem of approximating algebraic numbers is also studied as a case in the theory of transcendental numbers. Topics include the Thue-Siegel theorem, the Hermite-Lindemann theorem on the transcendency of the exponential function, and the work of C. Siegel on the transcendency of the Bessel functions and of the solutions of other differential equations. The final chapter considers the Gelfond-Schneider theorem on the transcendency of alpha to the power beta. Each proof is prefaced by a brief discussion of its scheme, which provides a helpful guide to understanding the proof's progression.
Author : Alan Baker
Publisher : Cambridge University Press
Page : pages
File Size : 19,66 MB
Release : 2022-06-09
Category : Mathematics
ISBN : 1009229966
First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue–Siegel–Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.
Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 39,50 MB
Release : 2001-02-22
Category : Mathematics
ISBN : 9780521004237
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author : David Angell
Publisher : CRC Press
Page : 243 pages
File Size : 31,21 MB
Release : 2021-12-30
Category : Mathematics
ISBN : 100052373X
Features Uses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation. Suitable as a primary textbook for advanced undergraduate courses in number theory, or as supplementary reading for interested postgraduates. Each chapter concludes with an appendix setting out the basic facts needed from each topic, so that the book is accessible to readers without any specific specialist background.
