Recurrence Sequences

By: Graham Everest, Alf van der Poorten, Igor Shparlinski, Thomas Ward

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Hardcover | 1 January 2003

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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.

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Non-Fiction Mathematics Number Theory Applied Mathematics Nonlinear Science Computing & I.T.Computer Science Mathematical Theory of Computation Calculus & Mathematical Analysis Optimisation Linear Programming

Notation
Introduction
Definitions and Techniques	p. 1
Zeros, Multiplicity and Growth	p. 25
Periodicity	p. 45
Operations on Power Series and Linear Recurrence Sequences	p. 65
Character Sums and Solutions of Congruences	p. 75
Arithmetic Structure of Recurrence Sequences	p. 93
Distribution in Finite Fields and Residue Rings	p. 117
Distribution Modulo 1 and Matrix Exponential Functions	p. 127
Applications to Other Sequences	p. 139
Elliptic Divisibility Sequences	p. 163
Sequences Arising in Graph Theory and Dynamics	p. 177
Finite Fields and Algebraic Number Fields	p. 191
Pseudo-Random Number Generators	p. 211
Computer Science and Coding Theory	p. 231
Sequences from the on-line Encyclopedia	p. 255
Bibliography	p. 257
Index	p. 309
Table of Contents provided by Blackwell. All Rights Reserved.

Recurrence Sequences

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