Everest G., van der Poorten A., Shparlinski I., Ward T. Recurrence Sequences

American Mathematical Society, 2003. — 318 p. — (Mathematical Surveys and Monographs 104). — ISBN: 0-8218-3387-1Definitions 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
Pseudo-Random Number Generators
Computer Science and Coding Theory
Sequences from the on-line EncyclopediaRecurrence 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.