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Recurrence Sequences

Graham Everest, Alf van der Poorten, Igor Shparlinski, Thomas Ward (Autoren)

Buch | Softcover

318 Seiten

2015
American Mathematical Society (Verlag)
978-1-4704-2315-5 (ISBN)

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Recurrence sequences 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 impact that methods from Diophantine analysis and transcendence theory have had on the subject.

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.

Graham Everest, University of East Anglia, Norwich, England. Alf van der Poorten and Igor Shparlinski, Macquarie University, Sydney, NSW, Australia. Thomas Ward, University of East Anglia, Norwich, England.

Definitions 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
Appendix: Sequences from the on-line encyclopedia
Bibliography
Index

Erscheinungsdatum	09.12.2015
Reihe/Serie	Mathematical Surveys and Monographs
Verlagsort	Providence
Sprache	englisch
Maße	152 x 229 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	1-4704-2315-4 / 1470423154
ISBN-13	978-1-4704-2315-5 / 9781470423155
Zustand	Neuware