Electronic ISBN:  9781470413316 
Product Code:  SURV/104.E 
List Price:  $92.00 
MAA Member Price:  $82.80 
AMS Member Price:  $73.60 

Book DetailsMathematical Surveys and MonographsVolume: 104; 2003; 318 ppMSC: Primary 11; 33; 37; 94;
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.
ReadershipResearch mathematicians interested in number theory, combinatorics, and graph theory.

Table of Contents

Chapters

1. Definitions and techniques

2. Zeros, multiplicity and growth

3. Periodicity

4. Operations on power series and linear recurrence sequences

5. Character sums and solutions of congruences

6. Arithmetic structure of recurrence sequences

7. Distribution in finite fields and residue rings

8. Distribution modulo 1 and matrix exponential functions

9. Applications to other sequences

10. Elliptic divisibility sequences

11. Sequences arising in graph theory and dynamics

12. Finite fields and algebraic number fields

13. Pseudorandom number generators

14. Computer science and coding theory


Additional Material

Reviews

The mathematical community should be grateful to the authors for the painstaking 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 wellwritten book will be extremely useful for anyone interested in any of the many aspects of linear recurrence sequences.
Mathematical Reviews


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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.
Research mathematicians interested in number theory, combinatorics, and graph theory.

Chapters

1. Definitions and techniques

2. Zeros, multiplicity and growth

3. Periodicity

4. Operations on power series and linear recurrence sequences

5. Character sums and solutions of congruences

6. Arithmetic structure of recurrence sequences

7. Distribution in finite fields and residue rings

8. Distribution modulo 1 and matrix exponential functions

9. Applications to other sequences

10. Elliptic divisibility sequences

11. Sequences arising in graph theory and dynamics

12. Finite fields and algebraic number fields

13. Pseudorandom number generators

14. Computer science and coding theory

The mathematical community should be grateful to the authors for the painstaking 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 wellwritten book will be extremely useful for anyone interested in any of the many aspects of linear recurrence sequences.
Mathematical Reviews