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There are well-known analogs of the prime number theorem and Mertensâ€™ theorem for dynamical systems with hyperbolic behaviour. Here we consider the same question for the simplest non-hyperbolicâ€¦ (More)

We introduce a class of group endomorphisms â€“ those of finite combinatorial rank â€“ exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, andâ€¦ (More)

- Shaun Stevens, Thomas Ward
- 2010

A dynamical Mertensâ€™ theorem for ergodic toral automorphisms with error term O(Nâˆ’1) is found, and the influence of resonances among the eigenvalues of unit modulus is examined. Examples are foundâ€¦ (More)

- Stephan Baier, SAWIAN JAIDEE, Shaun Stevens, Thomas Ward
- 2012

The dynamical Mertensâ€™ theorem describes asymptotics for the growth in the number of closed orbits in a dynamical system. We construct families of ergodic automorphisms of fixed entropy on compactâ€¦ (More)

- Shaun Stevens
- 2006

Let G be a unitary, symplectic or special orthogonal group over a locally compact nonarchimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G,â€¦ (More)

- Graham Everest, Shaun Stevens, Duncan Tamsett, Thomas Ward
- The American Mathematical Monthly
- 2007

will contain infinitely many prime terms â€” known as Mersenne primes. The Mersenne prime conjecture is related to a classical problem in number theory concerning perfect numbers. A whole number isâ€¦ (More)

The Local Converse Problem is to determine how the family of the local gamma factors Î³(s, Ï€ Ã— Ï„, Ïˆ) characterizes the isomorphism class of an irreducible admissible generic representation Ï€ of GLn(Fâ€¦ (More)

Let x(P ) = AP /B2 P denote the x-coordinate of the rational point P on an elliptic curve in Weierstrass form. We consider when BP can be a perfect power or a prime. Using Faltingsâ€™ theorem, we showâ€¦ (More)

An elliptic divisibility sequence, generated by a point in the image of a rational isogeny, is shown to possess a uniformly bounded number of prime terms. This result applies over the rationalâ€¦ (More)

- MOSHE ADRIAN, Baiying Liu, Shaun Stevens, X Peng
- 2014

Based on previous results of Jiang, Nien and the third author, we prove that any two minimax unitarizable supercuspidals of GLN that have the same depth and central character admit a special pair ofâ€¦ (More)