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Transcendental Numbers
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Andrei B. Shidlovskii
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Translated by:
Neal Koblitz
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Preface by:
W. D. Brownawell
Language:
English
Published/Copyright:
1989
Reviews
"The present book on transcendental numbers presents in a clear and beautiful way the method developed by Siegel, and later considerably improved by the author himself, for the consideration of the arithmetic properties of E-functions.[...] Using this book one can study this topic of transcendental number theory well, and the book is also very useful for mathematicians working in this field, too." Mathematical Reviews
Topics
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Frontmatter
I -
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Foreword
V -
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Preface to the English edition
IX -
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Preface
XI -
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Notation
XVIII -
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Introduction
1 -
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Chapter 1: Approximation of real and algebraic numbers
11 -
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Chapter 2: Arithmetic properties of the values of the exponential function at algebraic points
41 -
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Chapter 3: Transcendence and algebraic independence of the values of Ε-functions which are not connected by algebraic equations over the field of rational functions
79 -
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Chapter 4: Transcendence and algebraic independence of the values of Ε-functions which are connected by algebraic equations over the field of rational functions
128 -
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Chapter 5: Transcendence and algebraic independence of the values of Ε-functions which satisfy first order linear differential equations
179 -
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Chapter 6: Algebraic independence of the values of E-functions which satisfy second order linear differential equations
207 -
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Chapter 7: Solutions of certain linear differential equations of arbitrary order
232 -
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Chapter 8: Arithmetic methods applied to solutions of linear differential equations of arbitrary order
249 -
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Chapter 9: Siegel's Theorem
271 -
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Chapter 10: Solutions of linear differential equations of prime order p
307 -
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Chapter 11: The algebraic independence measure of values of IE-functions
349 -
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Chapter 12: The algebraic independence measure of values of KE-functions
378 -
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Chapter 13: Effective bounds for measures
405 -
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Concluding remarks
436 -
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Supplementary remarks on recent work for the English edition
444 -
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Bibliography
452 -
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Backmatter
467
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 1, 2011
eBook ISBN:
9783110889055
Hardcover published on:
December 1, 1989
Hardcover ISBN:
9783110115680
Edition:
Reprint 2011
Pages and Images/Illustrations in book
Front matter:
19
Main content:
466
Keywords for this book
Numbers, Transcendental
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
