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Recurrence Sequences (2003)
Book
Everest, G., van der Poorten, A., Shparlinski, I., & Ward, T. (2003). Recurrence Sequences. American Mathematical Society

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 r... Read More about Recurrence Sequences.

A higher-rank Mersenne problem (2002)
Book Chapter
Everest, G., Rogers, P., & Ward, T. (2002). A higher-rank Mersenne problem. In C. Fieker, & D. Kohel (Eds.), Algorithmic number theory (95-107). Springer Verlag. https://doi.org/10.1007/3-540-45455-1_8

The classical Mersenne problem has been a stimulating challenge to number theorists and computer scientists for many years. After briefly reviewing some of the natural settings in which this problem appears as a special case, we introduce an analogue... Read More about A higher-rank Mersenne problem.

Integer sequences and periodic points (2002)
Journal Article
Everest, G., van der Poorten, A., Puri, Y., & Ward, T. (2002). Integer sequences and periodic points. Journal of integer sequences, 5, Article 02.2.3

Arithmetic properties of integer sequences counting periodic points are studied, and applied to the case of linear recurrence sequences, Bernoulli numerators, and Bernoulli denominators.

Expansive subdynamics for algebraic Z^d-actions (2001)
Journal Article
Einsiedler, M., Lind, D., Miles, R., & Ward, T. (2001). Expansive subdynamics for algebraic Z^d-actions. Ergodic Theory and Dynamical Systems, 21(6), 1695-1729. https://doi.org/10.1017/s014338570100181x

A general framework for investigating topological actions of Z^d on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower dimensional subspaces of R^d. Here we completely describe this expansive behavior for... Read More about Expansive subdynamics for algebraic Z^d-actions.

Entropy and the canonical height (2001)
Journal Article
Einsiedler, M., Everest, G., & Ward, T. (2001). Entropy and the canonical height. Journal of Number Theory, 91(2), 256-273. https://doi.org/10.1006/jnth.2001.2682

The height of an algebraic number in the sense of Diophantine geometry is a measure of arithmetic complexity. There is a well-known relationship between the entropy of automorphisms of solenoids and classical heights. We consider an elliptic analogue... Read More about Entropy and the canonical height.

A dynamical property unique to the Lucas sequence (2001)
Journal Article
Puri, Y., & Ward, T. (2001). A dynamical property unique to the Lucas sequence. The Fibonacci quarterly, 39(5), 398-402

The only recurrence sequence satisfying the Fibonacci recurrence and realizable as the number of periodic points of a map is (a multiple of) the Lucas sequence.

Primes in elliptic divisibility sequences (2001)
Journal Article
Einsiedler, M., Everest, G., & Ward, T. (2001). Primes in elliptic divisibility sequences. LMS journal of computation and mathematics, 4, 1-13. https://doi.org/10.1112/s1461157000000772

Morgan Ward pursued the study of elliptic divisibility sequences initiated by Lucas, and Chudnovsky and Chudnovsky suggested looking at elliptic divisibility sequences for prime appearance. The problem of prime appearance in these sequences is examin... Read More about Primes in elliptic divisibility sequences.

Primes in divisibility sequences (2001)
Journal Article
Everest, G., & Ward, T. (2001). Primes in divisibility sequences. Cubo (Temuco. Print), 3(2), 245-259

We give an overview of two important families of divisibility sequences: the Lehmer--Pierce family (which generalise the Mersenne sequence) and the elliptic divisibility sequences. Recent computational work is described, as well as some of the mathem... Read More about Primes in divisibility sequences.

The canonical height of an algebraic point on an elliptic curve (2000)
Journal Article
Everest, G., & Ward, T. (2000). The canonical height of an algebraic point on an elliptic curve. New York journal of mathematics, 6, 331-342

We use elliptic divisibility sequences to describe a method for estimating the global canonical height of an algebraic point on an elliptic curve. This method requires almost no knowledge of the number field or the curve, is simple to implement, and... Read More about The canonical height of an algebraic point on an elliptic curve.