國立虎尾科技大學 |

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:	Approximation 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:

527707
Approximation theory.

LC Class. No.: QA221 / .B78 2004

Dewey Class. No.: 512.7/4

Approximation by algebraic numbers /
LDR:02555nam a2200313 i 4500 001 1124557
003 UkCbUP
005 20151005020624.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 240926s2004||||enk o ||1 0|eng|d
020 $a 9780511542886 (ebook)
020 $z 9780521823296 (hardback)
020 $z 9780521045674 (paperback)
035 $a CR9780511542886
040 $a UkCbUP $b eng $e rda $c UkCbUP
050 0 0 $a QA221 $b .B78 2004
082 0 0 $a 512.7/4 $2 22
100 1 $a Bugeaud, Yann, $d 1971- $e author. $3 1442158
245 1 0 $a Approximation by algebraic numbers / $c Yann Bugeaud.
264 1 $a Cambridge : $b Cambridge University Press, $c 2004.
300 $a 1 online resource (xv, 274 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
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 Approximation theory. $3 527707
650 0 $a Algebraic number theory. $3 672442
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