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 distribution...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2012
|
| Schriftenreihe: | Cambridge tracts in mathematics
193 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1017/CBO9781139017732 https://doi.org/10.1017/CBO9781139017732 https://doi.org/10.1017/CBO9781139017732 https://doi.org/10.1017/CBO9781139017732 |
| 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 |
| Umfang: | 1 Online-Ressource (xvi, 300 Seiten) |
| ISBN: | 9781139017732 |
| DOI: | 10.1017/CBO9781139017732 |
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| 505 | 8 | |a Distribution modulo one -- On the fractional parts of powers of real numbers -- On the fractional parts of powers of algebraic numbers -- Normal numbers -- Further explicit constructions of normal and non-normal numbers -- Normality to different bases -- Diophantine approximation and digital properties -- Digital expansion of algebraic numbers -- Continued fraction expansions and beta-expansions -- Conjectures and open questions -- Combinatorics on words -- Some elementary lemmata -- Measure theory -- Continued fractions -- Diophantine approximation -- 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 | ||
| 650 | 4 | |a Diophantine analysis | |
| 650 | 4 | |a Distribution modulo one | |
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| author | Bugeaud, Yann 1971- |
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| contents | Distribution modulo one -- On the fractional parts of powers of real numbers -- On the fractional parts of powers of algebraic numbers -- Normal numbers -- Further explicit constructions of normal and non-normal numbers -- Normality to different bases -- Diophantine approximation and digital properties -- Digital expansion of algebraic numbers -- Continued fraction expansions and beta-expansions -- Conjectures and open questions -- Combinatorics on words -- Some elementary lemmata -- Measure theory -- Continued fractions -- Diophantine approximation -- Recurrence sequences |
| ctrlnum | (ZDB-20-CBO)CR9781139017732 (OCoLC)967601901 (DE-599)BVBBV043942272 |
| 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/CBO9781139017732 |
| format | Electronic eBook |
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| id | DE-604.BV043942272 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:18Z |
| institution | BVB |
| isbn | 9781139017732 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351241 |
| oclc_num | 967601901 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xvi, 300 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 | 2012 |
| publishDateSearch | 2012 |
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| publisher | Cambridge University Press |
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| series2 | Cambridge tracts in mathematics |
| spelling | Bugeaud, Yann 1971- Verfasser (DE-588)173723802 aut Distribution modulo one and diophantine approximation Yann Bugeaud Distribution Modulo One & Diophantine Approximation Cambridge Cambridge University Press 2012 1 Online-Ressource (xvi, 300 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 193 Distribution modulo one -- On the fractional parts of powers of real numbers -- On the fractional parts of powers of algebraic numbers -- Normal numbers -- Further explicit constructions of normal and non-normal numbers -- Normality to different bases -- Diophantine approximation and digital properties -- Digital expansion of algebraic numbers -- Continued fraction expansions and beta-expansions -- Conjectures and open questions -- Combinatorics on words -- Some elementary lemmata -- Measure theory -- Continued fractions -- Diophantine approximation -- 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 Diophantine analysis Distribution modulo one Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-11169-0 Erscheint auch als Druck-Ausgabe 978-0-521-12887-2 https://doi.org/10.1017/CBO9781139017732 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Bugeaud, Yann 1971- Distribution modulo one and diophantine approximation Distribution modulo one -- On the fractional parts of powers of real numbers -- On the fractional parts of powers of algebraic numbers -- Normal numbers -- Further explicit constructions of normal and non-normal numbers -- Normality to different bases -- Diophantine approximation and digital properties -- Digital expansion of algebraic numbers -- Continued fraction expansions and beta-expansions -- Conjectures and open questions -- Combinatorics on words -- Some elementary lemmata -- Measure theory -- Continued fractions -- Diophantine approximation -- Recurrence sequences Diophantine analysis Distribution modulo one Diophantische Approximation (DE-588)4135760-7 gnd |
| subject_GND | (DE-588)4135760-7 |
| title | Distribution modulo one and diophantine approximation |
| title_alt | Distribution Modulo One & 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 Yann Bugeaud |
| title_fullStr | Distribution modulo one and diophantine approximation Yann Bugeaud |
| title_full_unstemmed | Distribution modulo one and diophantine approximation Yann Bugeaud |
| title_short | Distribution modulo one and diophantine approximation |
| title_sort | distribution modulo one and diophantine approximation |
| topic | Diophantine analysis Distribution modulo one Diophantische Approximation (DE-588)4135760-7 gnd |
| topic_facet | Diophantine analysis Distribution modulo one Diophantische Approximation |
| url | https://doi.org/10.1017/CBO9781139017732 |
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