MARC Record from Library of Congress

LEADER: 02602cam a2200301 a 4500
001 2012013417
003 DLC
005 20121220084154.0
008 120409s2012 nyu b 001 0 eng
010 $a 2012013417
020 $a9780521111690 (hardback)
040 $aDLC$cDLC$dDLC
042 $apcc
050 00 $aQA242$b.B84 2012
082 00 $a512.7/4$223
084 $aMAT022000$2bisacsh
100 1 $aBugeaud, Yann,$d1971-
245 10 $aDistribution modulo one and diophantine approximation /$cYann Bugeaud.
260 $aNew York :$bCambridge University Press,$c2012.
300 $axvi, 300 p. ;$c24 cm.
490 0 $aCambridge tracts in mathematics ;$v193
520 $a"This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral powers of 3/2 and the frequency of occurrence of each digit in the decimal expansion of the square root of two. The author takes a point of view from combinatorics on words and introduces a variety of techniques, including explicit constructions of normal numbers, Schmidt's games, Riesz product measures and transcendence results. With numerous exercises, the book is ideal for graduate courses on Diophantine approximation or as an introduction to distribution modulo one for non-experts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references"--$cProvided by publisher.
504 $aIncludes bibliographical references and index.
505 8 $aMachine generated contents note: 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; References; Index.
650 0 $aDiophantine analysis.
650 0 $aDistribution modulo one.
650 7 $aMATHEMATICS / Number Theory$2bisacsh.
856 42 $3Cover image$uhttp://assets.cambridge.org/97805211/11690/cover/9780521111690.jpg