Approximation by algebraic 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 K...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
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| Schriftenreihe: | Cambridge tracts in mathematics
160 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 URL des Erstveröffentlichers |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 Online-Ressource (xv, 274 Seiten) |
| ISBN: | 9780511542886 |
| DOI: | 10.1017/CBO9780511542886 |
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| 505 | 8 | |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 | 4 | |a Approximation theory | |
| 650 | 4 | |a Algebraic number theory | |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Bugeaud, Yann 1971- |
| author_GND | (DE-588)173723802 |
| author_facet | Bugeaud, Yann 1971- |
| author_role | aut |
| author_sort | Bugeaud, Yann 1971- |
| author_variant | y b yb |
| building | Verbundindex |
| bvnumber | BV043941804 |
| classification_rvk | SK 470 SK 180 |
| collection | ZDB-20-CBO |
| contents | 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511542886 (OCoLC)850178649 (DE-599)BVBBV043941804 |
| dewey-full | 512.7/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/4 |
| dewey-search | 512.7/4 |
| dewey-sort | 3512.7 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511542886 |
| format | Electronic eBook |
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| id | DE-604.BV043941804 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511542886 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350774 |
| oclc_num | 850178649 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xv, 274 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Bugeaud, Yann 1971- Verfasser (DE-588)173723802 aut Approximation by algebraic numbers Yann Bugeaud Cambridge Cambridge University Press 2004 1 Online-Ressource (xv, 274 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 160 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 Approximation theory Algebraic number theory Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Algebraische Zahl (DE-588)4141847-5 gnd rswk-swf Algebraische Zahl (DE-588)4141847-5 s Approximationstheorie (DE-588)4120913-8 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-82329-6 Erscheint auch als Druck-Ausgabe 978-0-521-04567-4 https://doi.org/10.1017/CBO9780511542886 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Bugeaud, Yann 1971- Approximation by algebraic numbers 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 Approximation theory Algebraic number theory Approximationstheorie (DE-588)4120913-8 gnd Algebraische Zahl (DE-588)4141847-5 gnd |
| subject_GND | (DE-588)4120913-8 (DE-588)4141847-5 |
| title | Approximation by algebraic numbers |
| title_auth | Approximation by algebraic numbers |
| title_exact_search | Approximation by algebraic numbers |
| title_full | Approximation by algebraic numbers Yann Bugeaud |
| title_fullStr | Approximation by algebraic numbers Yann Bugeaud |
| title_full_unstemmed | Approximation by algebraic numbers Yann Bugeaud |
| title_short | Approximation by algebraic numbers |
| title_sort | approximation by algebraic numbers |
| topic | Approximation theory Algebraic number theory Approximationstheorie (DE-588)4120913-8 gnd Algebraische Zahl (DE-588)4141847-5 gnd |
| topic_facet | Approximation theory Algebraic number theory Approximationstheorie Algebraische Zahl |
| url | https://doi.org/10.1017/CBO9780511542886 |
| work_keys_str_mv | AT bugeaudyann approximationbyalgebraicnumbers |