Distribution Modulo One and Diophantine Approximation

Informationen zum Autor Yann Bugeaud is a Professor in the Institut de Recherche Mathématique Avancée (IRMA) at the University of Strasbourg, France. Klappentext A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, with exercises and open problems. "The reader may learn a lot from this book about various techniques used i this subject over many years (e.g., classical and metrical Diophantine approximation, combinatorics on words) and, in addition, find the proofs of some very recent results." - Arturas Dubickas, Mathematical Reviews Zusammenfassung A treatment of cutting-edge research on the distribution modulo one of sequences and related topics! much of it from the last decade. There are numerous exercises to aid student understanding of the topic! and researchers will appreciate the notes at the end of each chapter! extensive references and open problems. Inhaltsverzeichnis 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.

Klappentext
A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, with exercises and open problems.

Inhalt
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.

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