Page 1 Next

Displaying 1 – 20 of 159

Showing per page

Arithmetic progressions and the primes.

Terence Tao (2006)

Collectanea Mathematica

We describe some of the machinery behind recent progress in establishing infinitely many arithmetic progressions of length k in various sets of integers, in particular in arbitrary dense subsets of the integers, and in the primes.

Automorphisms with exotic orbit growth

Stephan Baier, Sawian Jaidee, Shaun Stevens, Thomas Ward (2013)

Acta Arithmetica

The dynamical Mertens' 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 compact connected groups with a continuum of growth rates on two different growth scales. This shows in particular that the space of all ergodic algebraic dynamical systems modulo the equivalence of shared orbit-growth asymptotics is not countable. In contrast, for the equivalence relation of measurable isomorphism...

Currently displaying 1 – 20 of 159

Page 1 Next