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Author: Alan Baker
Publisher: Cambridge University Press
ISBN: 1009229966
Category : Mathematics
Languages : en
Pages :
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Book Description
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: Alan Baker
Publisher: Cambridge University Press
ISBN: 1009229966
Category : Mathematics
Languages : en
Pages :
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Book Description
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: A. O. Gelfond
Publisher: Courier Dover Publications
ISBN: 0486802256
Category : Mathematics
Languages : en
Pages : 212
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Book Description
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: Yann Bugeaud
Publisher: Cambridge University Press
ISBN: 1139455672
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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: Aleksandr Osipovich Gelʹfond
Publisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 52
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Book Description
Author: Aleksandr Osipovich Gelʹfond
Publisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 45
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Book Description
Author: M. Ram Murty
Publisher: Springer
ISBN: 1493908324
Category : Mathematics
Languages : en
Pages : 219
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Book Description
This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.
Author: Alan Baker
Publisher: Cambridge University Press
ISBN: 100922994X
Category : Computers
Languages : en
Pages : 185
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Book Description
Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.
Author: Aleksandr Osipovich Gelʹfond
Publisher:
ISBN:
Category : Number theory
Languages : en
Pages : 45
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Book Description
Author: Michel Waldschmidt
Publisher: Springer Science & Business Media
ISBN: 3662115697
Category : Mathematics
Languages : en
Pages : 649
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Book Description
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: Aleksandr Osipovich Gelʹfond
Publisher:
ISBN:
Category : Transcendental numbers
Languages : en
Pages : 45
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Book Description
