000			02879nam a22003858i 4500
001			CR9781139017732
003			UkCbUP
005			20200124160240.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			110216s2012||||enk o ||1 0|eng|d
020			_a9781139017732 (ebook)
020			_z9780521111690 (hardback)
020			_z9780521128872 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA242 _b.B84 2012
082	0	0	_a512.7/4 _223
100	1		_aBugeaud, Yann, _d1971- _eauthor.
245	1	0	_aDistribution modulo one and diophantine approximation / _cYann Bugeaud.
246	3		_aDistribution Modulo One & Diophantine Approximation
264		1	_aCambridge : _bCambridge University Press, _c2012.
300			_a1 online resource (xvi, 300 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v193
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aDistribution 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			_aThis 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		0	_aDiophantine analysis.
650		0	_aDistribution modulo one.
776	0	8	_iPrint version: _z9780521111690
830		0	_aCambridge tracts in mathematics ; _v193.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139017732
999			_c518480 _d518478