Contributions to the Theory of Transcendental Numbers PDF Download
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Author: Gregory Chudnovsky
Publisher: American Mathematical Soc.
ISBN: 0821815008
Category : Mathematics
Languages : en
Pages : 464
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Book Description
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: Gregory Chudnovsky
Publisher: American Mathematical Soc.
ISBN: 0821815008
Category : Mathematics
Languages : en
Pages : 464
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Book Description
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: 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: 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.N. Parshin
Publisher: Springer Science & Business Media
ISBN: 3662036444
Category : Mathematics
Languages : en
Pages : 351
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Book Description
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: Edward B. Burger
Publisher: Springer Science & Business Media
ISBN: 1475741146
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.
Author: Saradha Natarajan
Publisher: Springer Nature
ISBN: 9811541558
Category : Mathematics
Languages : en
Pages : 184
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Book Description
This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite–Lindemann–Weierstrass theorem, Gelfond–Schneider theorem, Schmidt’s subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker’s original results. This book presents Baker’s original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of “Exercises” and interesting information presented as “Notes,” intended to spark readers’ curiosity.
Author: A.N. Parshin
Publisher: Springer
ISBN: 9783540614678
Category : Mathematics
Languages : en
Pages : 345
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Book Description
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: Carl Ludwig Siegel
Publisher: Princeton University Press
ISBN: 1400882354
Category : Mathematics
Languages : en
Pages : 102
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Book Description
The description for this book, Transcendental Numbers. (AM-16), will be forthcoming.
Author: A. O. Gelfond
Publisher: Courier Dover Publications
ISBN: 0486802256
Category : Mathematics
Languages : en
Pages : 208
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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.