Mathematical Surveys and Monographs 2003; 318 pp; softcover Volume: 104 ISBN10: 1470423154 ISBN13: 9781470423155 List Price: US$92 Member Price: US$73.60 Order Code: SURV/104.S
 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. Readership Research mathematicians interested in number theory, combinatorics, and graph theory. 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 Table of Contents  Definitions and techniques
 Zeros, multiplicity and growth
 Periodicity
 Operations on power series and linear recurrence sequences
 Character sums and solutions of congruences
 Arithmetic structure of recurrence sequences
 Distribution in finite fields and residue rings
 Distribution modulo 1 and matrix exponential functions
 Applications to other sequences
 Elliptic divisibility sequences
 Sequences arising in graph theory and dynamics
 Finite fields and algebraic number fields
 Pseudorandom number generators
 Computer science and coding theory
 Appendix: Sequences from the online encyclopedia
 Bibliography
 Index
