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Approximation by algebraic numbers /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Approximation by algebraic numbers // Yann Bugeaud.
作者:	Bugeaud, Yann,
面頁冊數:	1 online resource (xv, 274 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Algebraic number theory. -
電子資源:	https://doi.org/10.1017/CBO9780511542886
ISBN:	9780511542886 (ebook)

Approximation by algebraic numbers /
Bugeaud, Yann,1971-

Approximation by algebraic numbers /Yann Bugeaud. - 1 online resource (xv, 274 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;160. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

1. Approximation by rational numbers -- 2. Approximation to algebraic numbers -- 3. The classifications of Mahler and Koksma -- 4. Mahler's conjecture on S-numbers -- 5. Hausdorff dimension of exceptional sets -- 6. Deeper results on the measure of exceptional sets -- 7. On T-numbers and U-numbers -- 8. Other classifications of real and complex numbers -- 9. Approximation in other fields -- 10. Conjectures and open questions -- App. A. Lemmas on polynomials -- App. B. Geometry of numbers.

Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs. Starting from continued fractions and Khintchine's theorem, Bugeaud introduces a variety of techniques, ranging from explicit constructions to metric number theory, including the theory of Hausdorff dimension. So armed, the reader is led to such celebrated advanced results as the proof of Mahler's conjecture on S-numbers, the Jarnik-Besicovitch theorem, and the existence of T-numbers. Brief consideration is given both to the p-adic and the formal power series cases. Thus the book can be used for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the rich and comprehensive list of more than 600 references.

ISBN: 9780511542886 (ebook)Subjects--Topical Terms:

672442
Algebraic number theory.

LC Class. No.: QA221 / .B78 2004

Dewey Class. No.: 512.7/4

Approximation by algebraic numbers /
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245 1 0 $a Approximation by algebraic numbers / $c Yann Bugeaud.
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300 $a 1 online resource (xv, 274 pages) : $b digital, PDF file(s).
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490 1 $a Cambridge tracts in mathematics ; $v 160
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 1. Approximation by rational numbers -- 2. Approximation to algebraic numbers -- 3. The classifications of Mahler and Koksma -- 4. Mahler's conjecture on S-numbers -- 5. Hausdorff dimension of exceptional sets -- 6. Deeper results on the measure of exceptional sets -- 7. On T-numbers and U-numbers -- 8. Other classifications of real and complex numbers -- 9. Approximation in other fields -- 10. Conjectures and open questions -- App. A. Lemmas on polynomials -- App. B. Geometry of numbers.
520 $a Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs. Starting from continued fractions and Khintchine's theorem, Bugeaud introduces a variety of techniques, ranging from explicit constructions to metric number theory, including the theory of Hausdorff dimension. So armed, the reader is led to such celebrated advanced results as the proof of Mahler's conjecture on S-numbers, the Jarnik-Besicovitch theorem, and the existence of T-numbers. Brief consideration is given both to the p-adic and the formal power series cases. Thus the book can be used for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the rich and comprehensive list of more than 600 references.
650 0 $a Algebraic number theory. $3 672442
650 0 $a Approximation theory. $3 527707
776 0 8 $i Print version: $z 9780521823296
830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511542886