Distribution Modulo One and Diophantine Approximation

ISBN-13: 9780521111690 / Angielski / Twarda / 2012 / 316 str.

Yann Bugeaud

Opis

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

Recenzje

"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

Spis treści

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.