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Distribution modulo one and diophant...

Bugeaud, Yann, (1971-)

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Distribution modulo one and diophantine approximation

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Distribution modulo one and diophantine approximation/ Yann Bugeaud.
其他題名:	Distribution Modulo One & Diophantine Approximation
作者:	Bugeaud, Yann,
出版者:	Cambridge :Cambridge University Press, : 2012.,
面頁冊數:	xvi, 300 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	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.
標題:	Diophantine analysis. -
電子資源:	https://doi.org/10.1017/CBO9781139017732
ISBN:	9781139017732

Distribution modulo one and diophantine approximation
Bugeaud, Yann,1971-

Distribution modulo one and diophantine approximation[electronic resource] /Distribution Modulo One & Diophantine ApproximationYann Bugeaud. - Cambridge :Cambridge University Press,2012. - xvi, 300 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;193. - Cambridge tracts in mathematics ;193..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9781139017732Subjects--Topical Terms:

540536
Diophantine analysis.

LC Class. No.: QA242 / .B84 2012

Dewey Class. No.: 512.74

Distribution modulo one and diophantine approximation
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490 1 $a Cambridge tracts in mathematics ; $v 193
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $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 0 $a Diophantine analysis. $3 540536
650 0 $a Distribution modulo one. $3 2012534
830 0 $a Cambridge tracts in mathematics ; $v 193. $3 3470479
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