C.I.M.E. Foundation Subseries

Diophantine Approximation

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 – July 6, 2000

Authors: Masser, D., Nesterenko, Y.V., Schlickewei, H.P., Schmidt, W.M., Waldschmidt, M.

Editors: Amoroso, Francesco, Zannier, Umberto (Eds.)

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About this book

Diophantine Approximation is a branch of Number Theory having its origins intheproblemofproducing“best”rationalapproximationstogivenrealn- bers. Since the early work of Lagrange on Pell’s equation and the pioneering work of Thue on the rational approximations to algebraic numbers of degree ? 3, it has been clear how, in addition to its own speci?c importance and - terest, the theory can have fundamental applications to classical diophantine problems in Number Theory. During the whole 20th century, until very recent times, this fruitful interplay went much further, also involving Transcend- tal Number Theory and leading to the solution of several central conjectures on diophantine equations and class number, and to other important achie- ments. These developments naturally raised further intensive research, so at the moment the subject is a most lively one. This motivated our proposal for a C. I. M. E. session, with the aim to make it available to a public wider than specialists an overview of the subject, with special emphasis on modern advances and techniques. Our project was kindly supported by the C. I. M. E. Committee and met with the interest of a largenumberofapplicants;forty-twoparticipantsfromseveralcountries,both graduatestudentsandseniormathematicians,intensivelyfollowedcoursesand seminars in a friendly and co-operative atmosphere. The main part of the session was arranged in four six-hours courses by Professors D. Masser (Basel), H. P. Schlickewei (Marburg), W. M. Schmidt (Boulder) and M. Waldschmidt (Paris VI). This volume contains expanded notes by the authors of the four courses, together with a paper by Professor Yu. V.

Table of contents (5 chapters)

  • Heights, Transcendence, and Linear Independence on Commutative Group Varieties

    Masser, David

    Pages 1-51

    Preview Buy Chapter 30,19 €
  • Linear Forms in Logarithms of Rational Numbers

    Nesterenko, Yuri

    Pages 53-106

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

    Schlickewei, Hans Peter

    Pages 107-170

    Preview Buy Chapter 30,19 €
  • Linear Recurrence Sequences

    Schmidt, Wolfgang M.

    Pages 171-247

    Preview Buy Chapter 30,19 €
  • Linear Independence Measures for Logarithms of Algebraic Numbers

    Waldschmidt, Michel

    Pages 249-344

    Preview Buy Chapter 30,19 €

Buy this book

eBook 47,59 €
price for Spain (gross)
  • ISBN 978-3-540-44979-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 59,23 €
price for Spain (gross)
  • ISBN 978-3-540-40392-0
  • 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
Diophantine Approximation
Book Subtitle
Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 – July 6, 2000
Authors
Editors
  • Francesco Amoroso
  • Umberto Zannier
Series Title
C.I.M.E. Foundation Subseries
Series Volume
1819
Copyright
2003
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-44979-9
DOI
10.1007/3-540-44979-5
Softcover ISBN
978-3-540-40392-0
Edition Number
1
Number of Pages
XI, 356
Number of Illustrations and Tables
1 illustrations in colour
Topics