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Hardcover ISBN:  9780821815007 
Product Code:  SURV/19 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412463 
Product Code:  SURV/19.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821815007 
eBook ISBN:  9781470412463 
Product Code:  SURV/19.B 
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MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 19; 1984; 450 ppMSC: Primary 11; Secondary 32
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

Chapters

Introduction: Algebraic independence of values of exponential and elliptic functions

1. Some analytic methods in the theory of transcendental numbers

2. Baker’s method in the theory of transcendental numbers

3. On the way to Schanuel’s conjecture

4. Criteria of algebraic independence of several numbers

5. Methods of the theory of transcendental numbers, Diophantine approximations and solutions of Diophantine equations

6. Some Diophantine problems

7. Transcendences arising from exponential and elliptic functions

8. Measure of the algebraic independence of periods and quasiperiods of elliptic curves

9. Another method for investigating the arithmetic nature of values of functions of a complex variable

Appendix: The Proof of extremality of certain manifolds


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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.

Chapters

Introduction: Algebraic independence of values of exponential and elliptic functions

1. Some analytic methods in the theory of transcendental numbers

2. Baker’s method in the theory of transcendental numbers

3. On the way to Schanuel’s conjecture

4. Criteria of algebraic independence of several numbers

5. Methods of the theory of transcendental numbers, Diophantine approximations and solutions of Diophantine equations

6. Some Diophantine problems

7. Transcendences arising from exponential and elliptic functions

8. Measure of the algebraic independence of periods and quasiperiods of elliptic curves

9. Another method for investigating the arithmetic nature of values of functions of a complex variable

Appendix: The Proof of extremality of certain manifolds