Recurrence Sequences (Mathematical Surveys and Monographs)
By Alf Van Der Poorten, Igor Shparlinski, Thomas Ward
* Publisher: American Mathematical Society
* Number Of Pages: 318
* Publication Date: 2003-08-01
* ISBN-10 / ASIN: 0821833871
* ISBN-13 / EAN: 9780821833872
Product Description:
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.
Table of Contents Notation Introduction Ch. 1 Definitions and Techniques 1 Ch. 2 Zeros, Multiplicity and Growth 25 Ch. 3 Periodicity 45 Ch. 4 Operations on Power Series and Linear Recurrence Sequences 65 Ch. 5 Character Sums and Solutions of Congruences 75 Ch. 6 Arithmetic Structure of Recurrence Sequences 93 Ch. 7 Distribution in Finite Fields and Residue Rings 117 Ch. 8 Distribution Modulo 1 and Matrix Exponential Functions 127 Ch. 9 Applications to Other Sequences 139 Ch. 10 Elliptic Divisibility Sequences 163 Ch. 11 Sequences Arising in Graph Theory and Dynamics 177 Ch. 12 Finite Fields and Algebraic Number Fields 191 Ch. 13 Pseudo-Random Number Generators 211 Ch. 14 Computer Science and Coding Theory 231 Sequences from the on-line Encyclopedia 255 Bibliography 257 Index 309
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