Diophantine Approximation

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

David Masser, Yuri V. Nesterenko, Hans Peter Schlickewei, Wolfgang M. Schmidt, Michel Waldschmidt (Autoren)

Francesco Amoroso, Umberto Zannier (Herausgeber)

Buch | Softcover

XI, 356 Seiten

2003 | 1. Softcover reprint of the original 1st ed. 2003
Springer Berlin (Verlag)
978-3-540-40392-0 (ISBN)

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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.

Heights, Transcendence, and Linear Independence on Commutative Group Varieties.- Linear Forms in Logarithms of Rational Numbers.- Approximation of Algebraic Numbers.- Linear Recurrence Sequences.- Linear Independence Measures for Logarithms of Algebraic Numbers.

Erscheint lt. Verlag	14.7.2003
Reihe/Serie	C.I.M.E. Foundation Subseries
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XI, 356 p. 1 illus. in color.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	522 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	11J68, 11J86, 11B37 • Algebra • Diophantine approximation • Equation • Linear Forms in Logarithms • Number Theory • Proof
ISBN-10	3-540-40392-2 / 3540403922
ISBN-13	978-3-540-40392-0 / 9783540403920
Zustand	Neuware