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Encyclopaedia of Mathematical Sciences

Number Theory IV

Transcendental Numbers

Editors: Parshin, A.N., Shafarevich, I.R. (Eds.)

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eBook 130,89 €
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  • ISBN 978-3-662-03644-0
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Hardcover 171,59 €
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  • ISBN 978-3-540-61467-8
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Softcover 171,59 €
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  • ISBN 978-3-642-08259-7
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About this book

This book is a survey of the most important directions of research in transcendental number theory. The central topics in this theory include proofs of irrationality and transcendence of various numbers, especially those that arise as the values of special functions. Questions of this sort go back to ancient times. An example is the old problem of squaring the circle, which Lindemann showed to be impossible in 1882, when he proved that $Öpi$ is a transcendental number. Euler's conjecture that the logarithm of an algebraic number to an algebraic base is transcendental was included in Hilbert's famous list of open problems; this conjecture was proved by Gel'fond and Schneider in 1934. A more recent result was ApÖ'ery's surprising proof of the irrationality of $Özeta(3)$ in 1979. The quantitative aspects of the theory have important applications to the study of Diophantine equations and other areas of number theory. For a reader interested in different branches of number theory, this monograph provides both an overview of the central ideas and techniques of transcendental number theory, and also a guide to the most important results.

Table of contents (7 chapters)

  • Introduction

    Parshin, A. N. (et al.)

    Pages 11-21

    Preview Buy Chapter 30,19 €
  • Approximation of Algebraic Numbers

    Parshin, A. N. (et al.)

    Pages 22-77

    Preview Buy Chapter 30,19 €
  • Effective Constructions in Transcendental Number Theory

    Parshin, A. N. (et al.)

    Pages 78-145

    Preview Buy Chapter 30,19 €
  • Hilbert’s Seventh Problem

    Parshin, A. N. (et al.)

    Pages 146-178

    Preview Buy Chapter 30,19 €
  • Multidimensional Generalization of Hilbert’s Seventh Problem

    Parshin, A. N. (et al.)

    Pages 179-208

    Preview Buy Chapter 30,19 €

Buy this book

eBook 130,89 €
price for Spain (gross)
  • ISBN 978-3-662-03644-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 171,59 €
price for Spain (gross)
  • ISBN 978-3-540-61467-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 171,59 €
price for Spain (gross)
  • ISBN 978-3-642-08259-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Number Theory IV
Book Subtitle
Transcendental Numbers
Editors
  • A.N. Parshin
  • I.R. Shafarevich
Translated by
Koblitz, N.
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
44
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-03644-0
DOI
10.1007/978-3-662-03644-0
Hardcover ISBN
978-3-540-61467-8
Softcover ISBN
978-3-642-08259-7
Series ISSN
0938-0396
Edition Number
1
Number of Pages
VII, 345
Additional Information
Original Russian edition published by VINITI, Moscow
Topics