**Mathematical Surveys and Monographs**

Volume: 104;
2003;
318 pp;

MSC: Primary 11; 33; 37; 94;

**Electronic ISBN: 978-1-4704-1331-6
Product Code: SURV/104.E**

List Price: $92.00

AMS Member Price: $73.60

MAA Member Price: $82.80

#### Supplemental Materials

# Recurrence Sequences

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*Graham Everest; Alf van der Poorten; Igor Shparlinski; Thomas Ward*

Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.

#### Reviews & Endorsements

The mathematical community should be grateful to the authors for the pains-taking work that they have done, and for the very useful book that they have produced as a result.

-- Bulletin of the London Mathematical Society

Surprisingly enough, there was no book in the literature entirely devoted to recurrence sequences … With the book under review, the authors fill this gap in a remarkable way … this well-written book will be extremely useful for anyone interested in any of the many aspects of linear recurrence sequences.

-- Mathematical Reviews

#### Table of Contents

# Table of Contents

## Recurrence Sequences

- Contents v6 free
- Notation vii8 free
- Introduction ix10 free
- Chapter 1. Definitions and Techniques 116 free
- Chapter 2. Zeros, Multiplicity and Growth 2540
- Chapter 3. Periodicity 4560
- Chapter 4. Operations on Power Series and Linear Recurrence Sequences 6580
- Chapter 5. Character Sums and Solutions of Congruences 7590
- Chapter 6. Arithmetic Structure of Recurrence Sequences 93108
- Chapter 7. Distribution in Finite Fields and Residue Rings 117132
- Chapter 8. Distribution Modulo 1 and Matrix Exponential Functions 127142
- Chapter 9. Applications to Other Sequences 139154
- Chapter 10. Elliptic Divisibility Sequences 163178
- Chapter 11. Sequences Arising in Graph Theory and Dynamics 177192
- Chapter 12. Finite Fields and Algebraic Number Fields 191206
- Chapter 13. Pseudo-Random Number Generators 211226
- Chapter 14. Computer Science and Coding Theory 231246
- Sequences from the on-line Encyclopedia 255270
- Bibliography 257272
- Index 309324 free