**Mathematical Surveys and Monographs**

Volume: 19;
1984;
450 pp;
Hardcover

MSC: Primary 11;
Secondary 32

**Print ISBN: 978-0-8218-1500-7
Product Code: SURV/19**

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MAA Member Price: $116.10

**Electronic ISBN: 978-1-4704-1246-3
Product Code: SURV/19.E**

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# Contributions to the Theory of Transcendental Numbers

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*Gregory V. Chudnovsky*

This volume consists of a collection of papers devoted primarily to
transcendental number theory and diophantine approximations written by the
author. Most of the materials included in this volume are English translations
of the author's Russian manuscripts, extensively rewritten and brought entirely
up to date. These papers and other papers included in this volume were
available to specialists in manuscript form, but this is the first time that
they have been collected and published.

Though the earlier papers have been preserved in the form in which they were
prepared initially, the volume is organized in such a way as to reflect recent
progress and to allow readers to follow recent developments in the field. As an
introductory guide to the volume, the author included an expanded and updated
text of his invited address on his work on the theory of transcendental numbers
to the 1978 International Congress of Mathematicians in Helsinki.

The appendix contains a paper on the extremality of certain multidimensional
manifolds prepared by A. I. Vinogradov and the author in 1976.

Chudnovsky received a MacArthur Foundation Fellowship in 1981.

#### Table of Contents

# Table of Contents

## Contributions to the Theory of Transcendental Numbers

- Table of Contents v6 free
- Preface vii8 free
- Introduction: Algebraic Independence of Values of Exponential and Elliptic Functions 114 free
- Chapter 1 Some Analytic Methods in the Theory of Transcendental Numbers 2740 free
- Chapter 2 Baker's Method in the Theory of Transcendental Numbers 123136
- Chapter 3 On the Way to Schanuel's Conjecture 145158
- Chapter 4 Criteria of Algebraic Independence of Several Numbers 177190
- Chapter 5 Methods of the Theory of Transcendental Numbers, Diophantine Approximations and Solutions of Diophantine Equations 217230
- Chapter 6 Some Diophantine Problems 265278
- Chapter 7 Transcendences Arising from Exponential and Elliptic Functions 297310
- Chapter 8 Measure of the Algebraic Independence of Periods and Quasi-Periods of Elliptic Curves 355368
- Chapter 9 Another Method for Investigating the Arithmetic Nature of Values of Functions of a Complex Variable 383396
- Appendix: The Proof of Extremality of Certain Manifolds 421434
- Index 449462