Recurrence Sequences

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American Mathematical Soc., 2003 - Mathematics - 318 pages
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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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Contents

Definitions and Techniques
1
Zeros Multiplicity and Growth
25
Periodicity
45
Operations on Power Series and Linear Recurrence Sequences
65
Character Sums and Solutions of Congruences
75
Arithmetic Structure of Recurrence Sequences
93
Distribution in Finite Fields and Residue Rings
117
Distribution Modulo 1 and Matrix Exponential Functions
127
Elliptic Divisibility Sequences
163
Sequences Arising in Graph Theory and Dynamics
177
Finite Fields and Algebraic Number Fields
191
PseudoRandom Number Generators
211
Computer Science and Coding Theory
231
Sequences from the online Encyclopedia
255
Index
309
Copyright

Applications to Other Sequences
139

Common terms and phrases

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