Transcendental Numbers

Andrei B. Shidlovskii

Book

Transcendental Numbers

Andrei B. Shidlovskii
Translated by: Neal Koblitz
Preface by: W. D. Brownawell

Language: English

Published/Copyright: 1989

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This book is in the series

Volume 12 | De Gruyter Studies in Mathematics

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

Mathematics Algebra and Number Theory

Frontmatter Requires Authentication Unlicensed Licensed	I
Foreword W. D. Brownawell Requires Authentication Unlicensed Licensed	V
Preface to the English edition Requires Authentication Unlicensed Licensed	IX
Preface Requires Authentication Unlicensed Licensed	XI
Notation Requires Authentication Unlicensed Licensed	XVIII
Introduction Requires Authentication Unlicensed Licensed	1
Chapter 1: Approximation of real and algebraic numbers Requires Authentication Unlicensed Licensed	11
Chapter 2: Arithmetic properties of the values of the exponential function at algebraic points Requires Authentication Unlicensed Licensed	41
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 Requires Authentication Unlicensed Licensed	79
Chapter 4: Transcendence and algebraic independence of the values of Ε-functions which are connected by algebraic equations over the field of rational functions Requires Authentication Unlicensed Licensed	128
Chapter 5: Transcendence and algebraic independence of the values of Ε-functions which satisfy first order linear differential equations Requires Authentication Unlicensed Licensed	179
Chapter 6: Algebraic independence of the values of E-functions which satisfy second order linear differential equations Requires Authentication Unlicensed Licensed	207
Chapter 7: Solutions of certain linear differential equations of arbitrary order Requires Authentication Unlicensed Licensed	232
Chapter 8: Arithmetic methods applied to solutions of linear differential equations of arbitrary order Requires Authentication Unlicensed Licensed	249
Chapter 9: Siegel's Theorem Requires Authentication Unlicensed Licensed	271
Chapter 10: Solutions of linear differential equations of prime order p Requires Authentication Unlicensed Licensed	307
Chapter 11: The algebraic independence measure of values of IE-functions Requires Authentication Unlicensed Licensed	349
Chapter 12: The algebraic independence measure of values of KE-functions Requires Authentication Unlicensed Licensed	378
Chapter 13: Effective bounds for measures Requires Authentication Unlicensed Licensed	405
Concluding remarks Requires Authentication Unlicensed Licensed	436
Supplementary remarks on recent work for the English edition Requires Authentication Unlicensed Licensed	444
Bibliography Requires Authentication Unlicensed Licensed	452
Backmatter Requires Authentication Unlicensed Licensed	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

https://doi.org/10.1515/9783110889055

eBook ISBN: 9783110889055

Hardcover ISBN: 9783110115680

Keywords for this book

Numbers, Transcendental

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Transcendental Numbers

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