Diophantine Approximation on Linear Algebraic Groups :Transcendence Properties of the Exponential Function in Several Variables - Grundlehren der mathematischen Wissenschaften

Diophantine Approximation on Linear Algebraic Groups

Diophantine Approximation on Linear Algebraic Groups :Transcendence Properties of the Exponential Function in Several Variables - Grundlehren der mathematischen Wissenschaften

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Published: 26 May, 2000
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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.
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More Details

Type Book
ISBN13 9783540667858
ISBN10 3540667857
Number Of Pages 633
Item Weight 1000 g
Publisher / Reseller Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Format hardback
Edition 2000 ed.
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Media Reviews

“This extensive monograph gives an excellent report on the present state of the art … . The reader having enough time and energy may learn from this carefully written book a great deal of modern transcendence theory from the very beginning. In this process, the many included exercises may be very helpful. Everybody interested in transcendence will certainly admire the author’s achievement to present such a clear and complete exposition of a topic growing so fast.” (P.Bundschuh, zbMATH 0944.11024, 2021)

"The present book is very nice to read, and gives a comprehensive overview of one wide aspect of Diophantine approximation. It includes the main achievements of the last several years, and points out the most interesting open questions. Moreover, each chapter is followed by numerous exercises, which provide an interesting complement of the main text. Many of them are adapted from original papers. Solutions are not given; however, there are helpful hints. This book is of great interest not only for experts in the field; it should also be recommended to anyone willing to have a taste of transcendental number theory. Undoubtedly, it will be very useful for anyone preparing a post-graduate course on Diophantine approximation."--MATHEMATICAL REVIEWS

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