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Diophantine Approximation: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 - July 6, 2000: 1819 (Lecture Notes in Mathematics) - Softcover

 
9783540403920: Diophantine Approximation: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 - July 6, 2000: 1819 (Lecture Notes in Mathematics)

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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.

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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.

Reseña del editor

The C.I.M.E. session in Diophantine Approximation, held in Cetraro (Italy) June 28 - July 6, 2000 focused on height theory, linear independence and transcendence in group varieties, Baker's method, approximations to algebraic numbers and applications to polynomial-exponential diophantine equations and to diophantine theory of linear recurrences. Very fine lectures by D. Masser, Y. Nesterenko, H.-P. Schlickewei, W.M. Schmidt and M. Waldschmidt have resulted giving a good overview of these topics, and describing central results, both classical and recent, emphasizing the new methods and ideas of the proofs rather than the details. They are addressed to a wide audience and do not require any prior specific knowledge.

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Taschenbuch. Zustand: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 372 pp. Englisch. Bestandsnummer des Verkäufers 9783540403920

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Bestandsnummer des Verkäufers 9783540403920

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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 372 pp. Englisch. Bestandsnummer des Verkäufers 9783540403920

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