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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Definitions and Techniques
Zeros Multiplicity and Growth
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
Recurrence Sequences Graham Everest Alf van der Poorten Igor ...
Operations on Power Series and Linear Recurrence Sequences .... The importance of recurrence sequences hardly needs to be explained. Their ...
www.mth.uea.ac.uk/ sequences/ out.pdf
Primitive Prime Divisors of First-Order Polynomial Recurrence ...
of linear recurrence sequences and for elliptic divisibility sequences. In ... In the case of nonlinear recurrence sequences, however, only elliptic di- ...
www.math.wisc.edu/ ~ono/ reu06ppdivisor.pdf
Everest, van der Poorten, Shparlinski, and Ward: Recurrence Sequences
Recurrence Sequences Graham Everest, Alf van der Poorten, Igor Shparlinski, and Thomas Ward. Publication Year: 2003 ISBN-10: 0-8218-3387-1 ...
www.ams.org/ bookpages/ surv-104/
ingentaconnect Primes Generated by Recurrence Sequences
Primes Generated by Recurrence Sequences. Authors: Everest, Graham; Stevens, Shaun; Tamsett, Duncan; Ward, Tom. Source: American Mathematical Monthly, ...
www.ingentaconnect.com/ content/ maa/ amm/ 2007/ 00000114/ 00000005/ art00003;jsessionid=21j0an2jr0gk3.alexandra?format=print
arxiv:math.NT/0412079 v2 2 Mar 2006
2 RECURRENCE SEQUENCES. For most people their first introduction ... Bilinear recurrence sequences. The theory of linear recurrence sequences ...
arxiv.org/ pdf/ math/ 0412079
concerning linear recurrence sequences. In the second half, several applications are ..... Thomas Ward, Recurrence sequences [reviewed by Pieter Moree] ...
[Technorati] Tag results for linear programming
Recurrence Sequences (Mathematical Surveys and Monographs) by Alf Van Der Poorten (Author), Igor Shparlinski (Author), Thomas Ward (Author), Graham Everest ...
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arxiv:math.NT/0510583 v1 27 Oct 2005
In order to describe the zero sets of linear recurrence sequences in positive .... Theorem 1.8 can be generalized to recurrence sequences in modules over F ...
arxiv.org/ pdf/ math/ 0510583.pdf