Distribution Modulo One and Diophantine Approximation.:
"This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distri...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2012.
|
| Schriftenreihe: | Cambridge tracts in mathematics.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral powers of 3/2 and the frequency of occurrence of each digit in the decimal expansion of the square root of two. The author takes a point of view from combinatorics on words and introduces a variety of techniques, including explicit constructions of normal numbers, Schmidt's games, Riesz product measures and transcendence results. With numerous exercises, the book is ideal for graduate courses on Diophantine approximation or as an introduction to distribution modulo one for non-experts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references"-- |
| Beschreibung: | 1 online resource (318 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139527804 1139527800 9781139525411 1139525417 9781139530088 1139530089 9781139017732 113901773X 9780521128872 0521128870 |
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| 100 | 1 | |a Bugeaud, Yann. | |
| 245 | 1 | 0 | |a Distribution Modulo One and Diophantine Approximation. |
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| 505 | 0 | |a 1. Distribution modulo one -- 2. On the fractional parts of powers of real numbers -- 3. On the fractional parts of powers of algebraic numbers -- 4. Normal numbers -- 5. Further explicit constructions of normal and non-normal numbers -- 6. Normality to different bases -- 7. Diophantine approximation and digital properties -- 8. Digital expansion of algebraic numbers -- 9. Continued fraction expansions and beta-expansions -- 10. Conjectures and open problems -- A. Combinatorics on words; B. Some elementary lemmata; C. Measure theory; D. Continued fractions; E. Diophantine approximation; F. Recurrence sequences. | |
| 520 | |a "This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral powers of 3/2 and the frequency of occurrence of each digit in the decimal expansion of the square root of two. The author takes a point of view from combinatorics on words and introduces a variety of techniques, including explicit constructions of normal numbers, Schmidt's games, Riesz product measures and transcendence results. With numerous exercises, the book is ideal for graduate courses on Diophantine approximation or as an introduction to distribution modulo one for non-experts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references"-- |c Provided by publisher. | ||
| 650 | 0 | |a Distribution modulo one. |0 http://id.loc.gov/authorities/subjects/sh85038546 | |
| 650 | 0 | |a Diophantine approximation. |0 http://id.loc.gov/authorities/subjects/sh85006189 | |
| 650 | 6 | |a Répartition modulo 1. | |
| 650 | 6 | |a Approximation diophantienne. | |
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| _version_ | 1816882202769620992 |
| adam_text | |
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| author | Bugeaud, Yann |
| author_facet | Bugeaud, Yann |
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| contents | 1. Distribution modulo one -- 2. On the fractional parts of powers of real numbers -- 3. On the fractional parts of powers of algebraic numbers -- 4. Normal numbers -- 5. Further explicit constructions of normal and non-normal numbers -- 6. Normality to different bases -- 7. Diophantine approximation and digital properties -- 8. Digital expansion of algebraic numbers -- 9. Continued fraction expansions and beta-expansions -- 10. Conjectures and open problems -- A. Combinatorics on words; B. Some elementary lemmata; C. Measure theory; D. Continued fractions; E. Diophantine approximation; F. Recurrence sequences. |
| ctrlnum | (OCoLC)804664814 |
| dewey-full | 512.73 512.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.73 512.74 |
| dewey-search | 512.73 512.74 |
| dewey-sort | 3512.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn804664814 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:24:52Z |
| institution | BVB |
| isbn | 9781139527804 1139527800 9781139525411 1139525417 9781139530088 1139530089 9781139017732 113901773X 9780521128872 0521128870 |
| language | English |
| oclc_num | 804664814 |
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| physical | 1 online resource (318 pages) |
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| publishDate | 2012 |
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| publisher | Cambridge University Press, |
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| series | Cambridge tracts in mathematics. |
| series2 | Cambridge Tracts in Mathematics ; |
| spelling | Bugeaud, Yann. Distribution Modulo One and Diophantine Approximation. Cambridge : Cambridge University Press, 2012. 1 online resource (318 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge Tracts in Mathematics ; v. 193 Print version record. Includes bibliographical references and index. 1. Distribution modulo one -- 2. On the fractional parts of powers of real numbers -- 3. On the fractional parts of powers of algebraic numbers -- 4. Normal numbers -- 5. Further explicit constructions of normal and non-normal numbers -- 6. Normality to different bases -- 7. Diophantine approximation and digital properties -- 8. Digital expansion of algebraic numbers -- 9. Continued fraction expansions and beta-expansions -- 10. Conjectures and open problems -- A. Combinatorics on words; B. Some elementary lemmata; C. Measure theory; D. Continued fractions; E. Diophantine approximation; F. Recurrence sequences. "This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral powers of 3/2 and the frequency of occurrence of each digit in the decimal expansion of the square root of two. The author takes a point of view from combinatorics on words and introduces a variety of techniques, including explicit constructions of normal numbers, Schmidt's games, Riesz product measures and transcendence results. With numerous exercises, the book is ideal for graduate courses on Diophantine approximation or as an introduction to distribution modulo one for non-experts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references"-- Provided by publisher. Distribution modulo one. http://id.loc.gov/authorities/subjects/sh85038546 Diophantine approximation. http://id.loc.gov/authorities/subjects/sh85006189 Répartition modulo 1. Approximation diophantienne. MATHEMATICS Number Theory. bisacsh Diophantine approximation fast Distribution modulo one fast Print version: Bugeaud, Yann. Distribution Modulo One and Diophantine Approximation. Cambridge : Cambridge University Press, ©2012 9780521111690 Cambridge tracts in mathematics. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=465744 Volltext |
| spellingShingle | Bugeaud, Yann Distribution Modulo One and Diophantine Approximation. Cambridge tracts in mathematics. 1. Distribution modulo one -- 2. On the fractional parts of powers of real numbers -- 3. On the fractional parts of powers of algebraic numbers -- 4. Normal numbers -- 5. Further explicit constructions of normal and non-normal numbers -- 6. Normality to different bases -- 7. Diophantine approximation and digital properties -- 8. Digital expansion of algebraic numbers -- 9. Continued fraction expansions and beta-expansions -- 10. Conjectures and open problems -- A. Combinatorics on words; B. Some elementary lemmata; C. Measure theory; D. Continued fractions; E. Diophantine approximation; F. Recurrence sequences. Distribution modulo one. http://id.loc.gov/authorities/subjects/sh85038546 Diophantine approximation. http://id.loc.gov/authorities/subjects/sh85006189 Répartition modulo 1. Approximation diophantienne. MATHEMATICS Number Theory. bisacsh Diophantine approximation fast Distribution modulo one fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85038546 http://id.loc.gov/authorities/subjects/sh85006189 |
| title | Distribution Modulo One and Diophantine Approximation. |
| title_auth | Distribution Modulo One and Diophantine Approximation. |
| title_exact_search | Distribution Modulo One and Diophantine Approximation. |
| title_full | Distribution Modulo One and Diophantine Approximation. |
| title_fullStr | Distribution Modulo One and Diophantine Approximation. |
| title_full_unstemmed | Distribution Modulo One and Diophantine Approximation. |
| title_short | Distribution Modulo One and Diophantine Approximation. |
| title_sort | distribution modulo one and diophantine approximation |
| topic | Distribution modulo one. http://id.loc.gov/authorities/subjects/sh85038546 Diophantine approximation. http://id.loc.gov/authorities/subjects/sh85006189 Répartition modulo 1. Approximation diophantienne. MATHEMATICS Number Theory. bisacsh Diophantine approximation fast Distribution modulo one fast |
| topic_facet | Distribution modulo one. Diophantine approximation. Répartition modulo 1. Approximation diophantienne. MATHEMATICS Number Theory. Diophantine approximation Distribution modulo one |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=465744 |
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